The Power of the Arrhenius Equation Chemistry

The Power of the Arrhenius Equation ChemistryThe Arrhenius Equation is a reference tool used in the study of the Earth's magnetic field and atmosphere. It has been in use since 1919, in fact. You may find yourself wanting to use this type of equation in your research for a number of reasons, such as:Have you ever wondered if there is any relationship between magnetic fields and the atmosphere in general? For instance, if the magnetic field were too high, wouldn't the air be repelled or deflected? How would you explain what happens with those tiny force fields that would be present in the inner workings of the Earth itself? These questions can be difficult to answer if the magnetic field is not measured by us.But we are an insignificant scientific sample when it comes to such questions. So how do we measure such a powerful force field and magnetic field? We can take advantage of that tremendous field of energy and convert it into useful information.Such is the power of the Arrhenius E quation. This equation is a scientific way of expressing the relationship between the Earth's energy fields and our atmosphere. The goal of the equation is to find out what is affecting the Earth's magnetic field and its environment and whether it can change.In order to do that, we must first determine what the Earth's magnetic field is. We do this using Arrhenius' formula. After which, we can determine if there is a change in the magnetic field that is impacting the atmosphere.To begin the process, we are going to find out the frequency of the electromagnetic waves that are being emitted by the Earth's core. By knowing this frequency, we can then calculate the amount of energy that has been produced within the Earth's core. By correlating the intensity of such energy and the intensity of the earth's magnetic field, we can begin to create equations that allow us to know what is happening. As we get closer to a magnetic reversal, we will also be able to conclude which direction the m agnetic field is changing. Then we can predict where the magnetic reversal will occur, which we will then be able to see.Without a magnetic field, the atmosphere is exposed to more radiation. This will cause the ozone layer to be destroyed, which will cause the depletion of the oxygen in the atmosphere. If the atmosphere becomes depleted of oxygen, we won't be able to breathe.

Neuro-what Why Neuroplasticity Is the Key to Making Your Smart Kid Even Smarter.

Neuro-what Why Neuroplasticity Is the Key to Making Your Smart Kid Even Smarter. Neuro-what? Why Neuroplasticity Is the Key to Making Your Smart Kid Even Smarter. What is neuroplasticity? Many of us can still remember hearing, “Don’t hold your breath until your face turns red! You’ll kill your brain cells and they’ll never grow back!” Growing up we knew our parents’ wisdom should typically be trusted, and you probably shouldn’t hold your breath until your face turns red. But as it turns out, we didn’t really need to worry about killing or stunting the growth of our brain cells. Not too long ago, even scientists thought the brain stopped developing in early childhood. It was commonly believed that genetics and genetics alone dictated our ability to learn. We’ve since discovered that the brain changes and develops throughout a person’s lifeâ€"a concept called neuroplasticity. Think of your brain like a forest. To navigate from one end of the forest to another, a deer cuts a path through the trees. As increasingly more animals follow that path, the grass gets worn down, and the path becomes clear and easy to follow. Without the repetitive steps of the deer and squirrels and rabbits, the path would become unpassable, overgrown with plants. A fox trying to cross the forest would not be able to find his way. As we learn, our brain grows by creating and strengthening pathways between brain cells. These pathways can be created and strengthened at any point in our life, but develop at a much faster rate in early childhood. We learn constantly when we are youngâ€"how to talk, how to walk, how to reactâ€"and pathways are thus continually created. As we grow, these pathways get pruned just as a gardener prunes a shrub, and our brain takes shape. The stronger the branch, the harder it is to trim. Developing strong pathways when our children are young can lead to lifelong benefits. How can you use neuroplasticity to help your children’s development? Treat the brain like a muscle. We know that children’s brains are ripe for development. Treat them like muscles and train them to get stronger. Just as consistently lifting weights will build stronger muscles, consistent study will build stronger pathways in the brain. Incorporate this daily practice into your routine by setting aside just a few minutes a day to complete daily math exercises , stick to a nightly story time, or practice flashcards. Before you know it, your children will be reading chapter books and multiplying fractions! Teach your children about the concepts of neuroplasticity and growth mindset. Simply teaching children that their efforts impact their abilities leads to increased learning! Growth mindset, a concept established by Dr. Carol Dweck, is the understanding that intelligence and abilities are not set in stone, but can be developed. As we’ve learned, this belief is proven through the science of neuroplasticity. And as Dr. Dweck learned, when students are taught about the concepts of growth mindset and neuroplasticity, they perform better in school. Here are some tips on how to teach your children: Recall a time they really struggled to learn something. “Remember the first time you tried to ride a bike without training wheels? You fell off so many times that your knees were all scraped up. Now you can ride circles around me!” Praise properly. Instead of praising a trait, “You’re so smart!” praise effort, “You worked really hard today!” Embrace mistakes. Let your children know that making a mistake is natural when they’re trying something new or difficult. Give an example of a time that you made a mistake, and how it helped you learn. It’s encouraging to know that we can continue to learn throughout our lives. You can teach an old dog new tricks after all! But why not take advantage of your child’s rapidly developing brain to maximize learning opportunities? Teach your children that they can learn anything if they set their minds to it, and they will benefit their entire lives. You might also be interested in: Motivating Children by Developing a Growth Mindset Mistakes Make the Student Ace the School Year with Kumons Study Tips Roundup Guest Tips: How to Make Your Sleep Routine Smarter for Your Child Neuro-what Why Neuroplasticity Is the Key to Making Your Smart Kid Even Smarter. Neuro-what? Why Neuroplasticity Is the Key to Making Your Smart Kid Even Smarter. What is neuroplasticity? Many of us can still remember hearing, “Don’t hold your breath until your face turns red! You’ll kill your brain cells and they’ll never grow back!” Growing up we knew our parents’ wisdom should typically be trusted, and you probably shouldn’t hold your breath until your face turns red. But as it turns out, we didn’t really need to worry about killing or stunting the growth of our brain cells. Not too long ago, even scientists thought the brain stopped developing in early childhood. It was commonly believed that genetics and genetics alone dictated our ability to learn. We’ve since discovered that the brain changes and develops throughout a person’s lifeâ€"a concept called neuroplasticity. Think of your brain like a forest. To navigate from one end of the forest to another, a deer cuts a path through the trees. As increasingly more animals follow that path, the grass gets worn down, and the path becomes clear and easy to follow. Without the repetitive steps of the deer and squirrels and rabbits, the path would become unpassable, overgrown with plants. A fox trying to cross the forest would not be able to find his way. As we learn, our brain grows by creating and strengthening pathways between brain cells. These pathways can be created and strengthened at any point in our life, but develop at a much faster rate in early childhood. We learn constantly when we are youngâ€"how to talk, how to walk, how to reactâ€"and pathways are thus continually created. As we grow, these pathways get pruned just as a gardener prunes a shrub, and our brain takes shape. The stronger the branch, the harder it is to trim. Developing strong pathways when our children are young can lead to lifelong benefits. How can you use neuroplasticity to help your children’s development? Treat the brain like a muscle. We know that children’s brains are ripe for development. Treat them like muscles and train them to get stronger. Just as consistently lifting weights will build stronger muscles, consistent study will build stronger pathways in the brain. Incorporate this daily practice into your routine by setting aside just a few minutes a day to complete daily math exercises , stick to a nightly story time, or practice flashcards. Before you know it, your children will be reading chapter books and multiplying fractions! Teach your children about the concepts of neuroplasticity and growth mindset. Simply teaching children that their efforts impact their abilities leads to increased learning! Growth mindset, a concept established by Dr. Carol Dweck, is the understanding that intelligence and abilities are not set in stone, but can be developed. As we’ve learned, this belief is proven through the science of neuroplasticity. And as Dr. Dweck learned, when students are taught about the concepts of growth mindset and neuroplasticity, they perform better in school. Here are some tips on how to teach your children: Recall a time they really struggled to learn something. “Remember the first time you tried to ride a bike without training wheels? You fell off so many times that your knees were all scraped up. Now you can ride circles around me!” Praise properly. Instead of praising a trait, “You’re so smart!” praise effort, “You worked really hard today!” Embrace mistakes. Let your children know that making a mistake is natural when they’re trying something new or difficult. Give an example of a time that you made a mistake, and how it helped you learn. It’s encouraging to know that we can continue to learn throughout our lives. You can teach an old dog new tricks after all! But why not take advantage of your child’s rapidly developing brain to maximize learning opportunities? Teach your children that they can learn anything if they set their minds to it, and they will benefit their entire lives. You might also be interested in: Motivating Children by Developing a Growth Mindset Mistakes Make the Student Ace the School Year with Kumons Study Tips Roundup Guest Tips: How to Make Your Sleep Routine Smarter for Your Child

Utilizing Taught With Barney To Learn English

Utilizing Taught With Barney To Learn EnglishTaught with Barney is a program that helps students learn all aspects of the English language. By learning through a progressive and easy to follow tutorial Barney is able to teach every aspect of the English language to people who have limited experience of language. The program also assists to introduce the student with the basic rules of grammar and vocabulary and also helps to develop the English speaking skills of the student.This is a program that can be used by everyone. It has many benefits, starting from building the confidence of a person when it comes to speaking English. The main purpose of this program is to enable a person to master his or her English grammar and by using it the student will be equipped with the basics of language. This has the major benefit of helping to understand how the English language is used.Another benefit of this program is that by using it you will be able to build the confidence in talking about yo ur experiences of living in England. Learning more on how to speak English properly is what needs to be done if you want to gain more self-confidence.After learning how to use the English language, using Barney to improve your speaking abilities is the most effective way to build confidence and fluency. The main goal of Barney is to help to make you realize how important is to maintain an adequate level of confidence and fluency. By doing the easy to follow tutorial that is provided you will be able to improve your speaking level.There are several other benefits of Barney that you will be able to enjoy after having gained confidence in speaking English. The main aim of the program is to empower you and empower your confidence. By building the confidence and fluency you will be able to enhance your overall communication abilities.In order to enhance your speaking skills, you need to engage yourself in the program that you will find online. To give you the ultimate advantage of Barney , you should start with a smaller amount so that you can build up your confidence before you begin a bigger one. Taught with Barney will provide you with a step by step tutorial for the learner.This will help to build your confidence and with time you will be able to comprehend the lessons taught in English. You will also have the opportunity to work with a tutor that is more experienced in speaking English. With the help of this program you will be able to enhance your communication skills as well as build your confidence that will enable you to improve your communication with others.

What Is An Analytical Chemistry Textbook PDF?

What Is An Analytical Chemistry Textbook PDF?An analytical chemistry textbook PDF is usually what is presented as an alternative to a traditional book when teaching your students. The result of having an alternative which the students will find more acceptable is lessened tension during the course and this is something which the teachers are interested in. It is also good to know that if there is a certain event in the career of the student, he or she may be able to get a particular method of treatment or knowledge since that is what they may want to do as well.Even if a student decides to go for a book to help them get through a particular phase in their career, it is still important to keep in mind that they can choose other books that are suitable for themselves. As you may already know, your textbook is not a guide or a brief but a strategy in a certain area of the course. Since it is one of the crucial tools, you must know what your textbook is all about and how it is presented. So you must know whether or not it is worth your while.You must remember that the purpose of the textbook is not only to tell you about the basic principles but it is also a reference that helps you in knowing the basics of a certain subject. When you read a book or a study guide you should make sure that you are actually reading the right part of the page or in the right paragraph and you should be able to get through the whole chapter, if it is really an entire chapter. You must not always rely on the looks of the book because there is a lot more than meets the eye and the textbook as a whole will look different from one person to another.When you are studying a subject, you should not only rely on what is written but also on the different perspective of the author and how they represent the things. There is always a book with a different way of looking at the world and that can make a big difference when it comes to comprehension and understanding.You must also make sure that th e book has been revised and you can tell the major changes by looking at the cover and inside of the book. Also take note of the author of the book, since that is a good sign that the book is worth your time and effort.When you are selecting a book, do not worry about the price of the book but rather concentrate on the quality of the book and the resources available. Many websites will allow you to choose the contents and the site will also provide you with the kind of book that you want to have. Of course you can always choose a special edition that is normally priced much higher.Finally, think about the education that the book provides and its importance to the future of your students. It will also be important to see whether or not you have options on what kind of textbook to buy since they come in various sizes and with various resources for your students.

The Best Way to Learn Spanish Formal Commands

The Best Way to Learn Spanish Formal Commands Maile Proctor Not sure when to use formal or informal commands in Spanish? Here, language teacher  Jason N.  shares his tips to help you understand the different types of commands, and the easy way to change Spanish verbs to commands When youre studying  Spanish you will learn about the different types of commands. Commands in Spanish arent as easy as they are in English. In English, theres no distinction between formal and informal commands. For example, to make the verb to run into a command, all you need to do is remove the to and simply say, run. Pretty simple, right? Commands arent as straightforward in Spanish. In order to understand Spanish formal commands and how they work, lets look at the distinction between informal and formal commands. You should use an informal command with someone you know well, like a friend, cousin, spouse or classmate. On the other hand, use a formal command with an older person, a superior, and people of high status like doctors, judges, priests, policemen, and lawyers.  If you don’t use formal commands with these types of people, you may unintentionally offend them by addressing them informally. Here is a closer look at Spanish formal commands, and a guide to converting verbs into commands. Using Spanish Formal Commands Use formal commands to show respect when you address a person.  If you want to convert a verb into a formal command, use these three steps: Remove the last two letters of the verb in its infinitive form. For example: Hablar = Habl Remember to flip the ending. The ending refers to whether the verb is ends in -ar or -ir/-er. If it ends in -ar, simply change the a to an e. If its an -er/-ir verb, change the i or e to an a. Add the new ending to the end of the word to create the formal command. Here are some examples: Step 1: Hablar  Habl, Step 2: the a becomes an e Step 3: Hable Step 1: Correr Corr Step 2: the e becomes an a Step 3: Corra Step 1: Vivir Viv Step 2: the i becomes an a Step 3: Viva Practice changing these verbs into commands: Beber Dudar Cambiar Recibir (beba, dude, cambie, reciba) Plural Commands To address more than one person, simply add an n to the formal Spanish command. Hable Hablen Corra Corran It seems pretty easy, right? It can get a little tricky when the verbs are stem-changers or irregular, but your Spanish tutor can help you understand these more complicated topics. For now, practice conjugating verbs into Spanish formal commands, and learn the appropriate times to use them. If you have any questions, make sure to write them down and go over them with a teacher or private tutor. Jason N. tutors in English and Spanish in Fairfax, CA.  He majored in Spanish at UC Davis, lived in Mexico for 3 years where he completed a Masters degree in Counseling, and studied Spanish Literature and Psychology at the University of Costa Rica. Learn more about Jason here!   Interested in Private Lessons? Search thousands of teachers for local and live, online lessons. Sign up for convenient, affordable private lessons today! Search for Your Teacher Photo by  LeafLanguages

A Guide to Observational Drawing

A Guide to Observational Drawing Observational Still Life  Drawing ChaptersWhat is Observational Drawing?The Right Brain’s Role in Realistic DrawingFollowing Step by Step Drawing InstructionsWhat Can Observational Drawing Do For You on a Personal Level?Observational drawing is a key part of learning to draw.It may not seem terribly interesting to draw a basket of fruit to practice your drawing skills, however, developing your sense of attention to detail is an essential step in mastering the basics if art!Realism in drawing involves a complex process, but this improves with practice.Faithfully reproducing an object with a pencil and paper involves carefully examining its characteristics to produce a portrait or landscape which looks realistic.Practicing realistic drawing exercises will give you a set of skills which are transferable to other types of drawing such as caricature and technical drawing.The Indian philosopher, Jiddu Krishnamurti, who was awarded the UN Peace Medal in 1984 said:The ability to observe without evaluating is the highest fo rm of intelligenceThis applies to observational drawing, which is all about observing without judgement and drawing what is in front of us, without getting carried away with our own ideas.This idea seems so simple; however, it may be more difficult than you think.Let’s take children’s young brains as an example, as they are less developed than the adult brain and are lacking in their capacity for detailed observation.If they’re given an object or scene to reproduce, children will tend away from drawing what they see, and choose to rely on what they already know. For instance, they may draw four wheels on a car, even if they can only see two, because they know that cars have four wheels.And the same goes for the left brain!The left brain has a lot of experience with real life and will, therefore, analyse visual perception rather than taking it as it is, producing an unfaithful picture which favours logic over reality.In order to truly learn how to effectively produce a realisti c drawing, you must force yourself to view things with a fresh pair of eyes, forgetting everything you’ve learnt so that it doesn’t inhibit your ability to take reality as you see it. The precision you achieve with life drawing will be very useful if you decide to go into the field of technical drawing.When training your eye, you only need a few drawing materials: paper, a pencil, pen and ink, a paintbrush or oil pastel.Following Step by Step Drawing InstructionsObservational freehand sketching happens in several steps.The two main ones are always the same:General contour of the object to be drawn using simple shapesAdding detailsRealistic drawing is all about working within a frame whilst respecting the proportions of the object and your perspective as an artist.For this reason, you must have made a final decision on what you want to draw before you begin drawing (objects should not be added in afterwards).Once you have traced your first outline of the object, you need to check that you have conformed to the rules of perspective, proportion and orientation.Working on Your Observational SkillsOnce you’ve finished the first step and you are happy with your contour drawing, you can begin to focus on the details of the object.Each individual element should be closely examined and compared with the other details that surround it.This kind of work requires the artist to have a good knowledge of drawing techniques and different ways of achieving realistic art. Drawing from life will help you advance in other techniques as well. A good caricaturist needs to understand how the human body works so it still looks recongnisable when it is distorted.If you would like to work on your ability to produce realistic work, you’ll need to practice working with different textures, and practicing your shading techniques to create depth within a picture as well as using negative space.When learning to draw, even easy practical exercises will help you develop a good sense of observation.Here are a few starting points:Draw without looking at the paper: This works on the principle that your hand should be an extension of your eye. So, tape your drawing paper or sketchbook to the table and have a go at drawing something in front of you!Invert your image: This technique helps to train the right brain. Choose an object, but reproduce it as if you’re seeing a mirror image. This helps you to disconnect your left brain from the drawing process and focus on what is in front of you.Practice drawing complex details: This is how you overcome artist’s block in your projects. Instead of drawing an arm attached to a body, just draw the shoulder on its own.Drawing What You Don’t SeeDon’t worry, this isn’t going to contradict everything that has just been said, even if it seems a little paradoxical. In order to draw what you see, you’ll also need to draw what you don’t see, at least upon your first glance.In observational drawing, looking at three dimensi onal objects requires a mastery of perspective, depth, proportion and line drawing.This is why it is essential to bear in mind the things that are hidden behind your object to produce a drawing that is faithful to real life.Let’s look at an example. You are tasked with drawing a person in front of a bookcase. If you focus on what you see, you’ll only draw one part of the furniture.The risk is that if you don’t look at the bookcase in its entirety, its shelves may not be perfectly aligned, and the drawing will become less realistic.Take the wave pattern into account, even though it's 'not there' ¦ source: Pixabay - Dan_ParkEven though the final piece will only show the part of the bookcase you are able to see, its closeness to reality depends on your ability to use its hidden parts as a guide.The same goes when drawing a human figure.Is one part of their arm hidden? Then you’ll need to know how it is placed behind them to make the drawing realistic. In other words, the invis ible structure influences the final appearance.Mastering this aspect of drawing will help you advance in other drawing techniques as well - varying your techniques will always teach you something new.What Can Observational Drawing Do For You on a Personal Level?Observational drawing is a very interesting exercise, even for amateur artists. It gives you a means of developing certain skills, including:Controlling your movementDeveloping observational skillsImproving capacity for concentrationRelaxingAs a hobby, it can also be particularly useful in day-to-day life. Realistic drawing is at the heart of a number of professions, such as:ScienceIllustration and digital drawingDesignArchitecturePortraiturePhotographyCaricature drawingSatirical drawingTechnical drawingThe skills you gain through your drawing lessons are many and varied, and can be transferred to many areas.They say practice makes perfect, and this is definitely true for drawing, and teaches you to take your time.Before you become a master, you need to be patient and work on your skills. Observational drawing may seem incredibly difficult, but it will set you up for success when it comes to other areas such as cartooning and impressionism.If you want to look at the art of drawing in detail, why not experiment with new techniques and tools?Use graphite pencil, colored pencils, watercolor paints, drawing software, charcoal pencil… the list is endless! Through experimentation, you’ll be able to find your style and the materials which suit you best.Find tutors all over the UK available for drawing lessons on Superprof:drawing lessons for kidsdrawing lessons onlinedrawing lessons for beginners

Mirror Formula

Mirror Formula Mirror Formula (Concave Mirror) Mirrors are a part of our life! It is quite natural for all of us to look at ourselves when we pass across a mirror. As common as it is to find a mirror or to look at our image, the science behind the mirror is actually fascinating. The mirrors which we use in our daily life are the flat or the plane mirrors (they are not curved), and any object in front of it appears exactly the same size in the mirror. The distance of the objects image is also formed exactly at the same distance behind the mirror as the distance the object is in front of the mirror. This phenomenon is explained by the laws of reflection. Laws of reflection applies to both flat mirrors and curved mirrors. The reflection of an object in a curved mirror forms an image which is not necessarily located at the same distance as the objects distance. Also, the image size is not necessarily the same as the objects size. However, these details can be estimated by using the Mirror Formula. In order to understand the mirror formula, let us first take a look at how an image is formed in a concave mirror. Curved Mirrors: The basic curved mirrors can be considered as a part of the spherical mirrors. It appears as though a spherical mirror has been sliced thus forming the two basic types of curved mirrors. When the inner curved surface is silvered to form a reflecting surface then it is the concave mirror, and when the outer surface of the curve is silvered to form a reflecting surface, then it is the convex mirror. The two basic types of curved mirrors are: i. Concave Mirror: A mirror that is curved inward and has a center that goes inward. ii. Convex Mirror: A mirror that is curved outward, and has a center that comes outward. What is a Concave Mirror? A Concave mirror is a mirror that is curved inward, and hence has the center that goes inward. A simple way to remember this is by taking the word cave from concave, and think that concave mirrors cave inward, just like you are looking inside a cave! For a concave mirror, the inner surface of the curve is silvered so that it forms the reflecting surface. In order to understand reflection upon a concave mirror, there are important terms to be understood. Center of Curvature: Considering that a concave mirror is actually a part of a sphere, the point which is the center of this sphere is known as the Center of Curvature C. Principal Axis: The line connecting the center of the sphere and the center of the mirror is the known as the Principal Axis. Vertex (or Pole): The point where the Principal Axis meets the mirror (the reflecting surface) is known as the Vertex or the Pole of the mirror. The vertex can also be defined as the center of the mirror taken geometrically. In the figure on the right, it is represented by the letter P. Radius of curvature: The distance from the center of curvature to the vertex is known as the radius of curvature, R. Focal point: The midpoint between the center of curvature and the vertex is known as the Focal point F. Focal distance (or focal length): The distance from the mirror to the focal point is known as the Focal distance, f. The Law of Reflection: Our eyes make it possible to see everything around us. But then why in dark, any object even in front of our eyes is not visible? This is because of the absence of light. When light falls on an object, it is reflected back and this reflected light rays reach our eyes and hence make the object visible to us. The Law of Reflection explains this behavior of light, and this law can be applied to both plane mirrors and curved mirrors. The ray of light that approaches a mirror is known as the Incident ray. The point at which the light ray strikes the mirror is known as the Point of Incidence. The ray of light that returns back from the mirror is known as the Reflected ray. At the point of incidence, the line drawn perpendicular to the surface of the mirror is known as the Normal line. The angle formed in between the incident ray and the reflected ray is divided by this normal line, and therefore 2 angles are formed. The angle formed in between the incident ray and the normal is known as the Angle of Incidence, and the angle formed in between the normal and the reflected ray is known as the Angle of Reflection. The Law of Reflection states that when a light ray reflects off a surface (flat or curved), then the angle of incidence is equal to the angle of reflection Angle of Incidence = Angle of Reflection Reflection in a Concave Mirror: The law of reflection of light is applied to both flat mirrors and curved mirrors. The reflection law helps us to determine the location of the image for a particular object. This image location is observed as the point where all the reflected light rays appear to be diverging. It is not an easy task to use the law of reflection in a curved mirror and estimate the image location. In order to do this, the normal line which is the line drawn at the point of incidence perpendicular to the curved surface must be drawn and then the law of reflection must be applied to determine the image location. The 2 rules which help us find the image location in a concave mirror are: i. If any incident ray travels parallel to the principal axis, then after reflection on the concave mirror its reflected ray will pass through the focal point. ii. If any incident ray passes through the focal point, then after reflection on the concave mirror its reflected ray will travel parallel to the principal axis. Characteristics of Image formed in Concave Mirrors: In order to determine the size of the image, orientation, location and the type of image formed by the reflection of the object in the concave mirrors, ray diagrams were constructed. Using the ray diagrams, the characteristics of the image for a certain object location can be described. Some of the important characteristics that are commonly analyzed from ray diagrams are: Location of the image relative to the objects location. Orientation of the image whether the image is upright or is inverted. Size of the image relative to the objects size whether it is reduced, magnified or is the same size as the object. Type of image formed whether the image is a real image or is a virtual image. There are 5 general locations where the object is placed, and with respect to these locations the characteristics of the image are observed. Location 1: The object is placed beyond the Center of Curvature If the object is placed beyond the center of curvature C, then the image will be formed at a location in between the center of curvature and the focal point. The orientation of the image is inverted, and therefore in this case an inverted image is formed. The size of the image is reduced, which implies that the image formed is smaller in dimensions than the objects dimensions. The type of image formed in this case is a real image. This is because the light rays converge at the image location due to which a real image is formed. To observe this practically, a sheet of paper can be placed at the location of the image and it will be observed that the replica of the object (reduced in size) would appear on the paper. Location 2: The object is placed at the center of curvature If the object is located at the center of curvature C, then the image is also formed at the center of curvature. The orientation of the image is inverted, and therefore in this case an inverted image is formed. The size of the image is exactly the same as the size of the object. Therefore the object and image have same dimensions. The image formed in this case is a real image as the light rays converge at the location of the image. This implies that the formed image can be practically observed on the sheet of paper when the paper is placed at the image location. Location 3: The object is located in between the center of curvature and the focal point If the object is located in anywhere between the center of curvature C and the focal point F, then the image is formed beyond the center of curvature. The orientation of the image is inverted and therefore in this case an inverted image is formed. The size of the image is magnified in this case. This implies that the formed image will have dimensions greater than the objects dimensions. The image formed in this case is a real image. This is because the rays of light converge at the location of the image and therefore the image can be practically observed on a sheet of paper when the paper is placed at the image location. Location 4: The object is placed at the focal point If the object is located at the focal point, then there is no image formed. This is because the rays of light from the focal point (which also happen to be the objects location) will reflect upon the mirror and will neither converge nor diverge. After reflection, these reflected rays travel parallel to each other and therefore no image is formed. Location 5: The object is placed in front of the focal point If the object is placed anywhere in front of the focal point, then the image will be always formed on the opposite side of the concave mirror. The orientation of the image is upright, which implies that the image is not inverted and is upright just like the object. The size of the image formed in this case is magnified. This implies that the dimensions of the image are greater than the dimensions of the object. The type of image formed in this case is a virtual image. This is because the rays of light after reflection upon the concave mirror diverge. In order to get the point of intersection of these diverging rays, the reflected rays are extended backwards and this takes us behind the mirror. This point of intersection of the reflected rays is the image location and since it is formed behind the mirror, hence it is a virtual image. In this case there will be no image formed on the sheet of paper as light does not actually pass through the location of the image. Mirror Formula: Ray diagrams are extremely helpful in trying to understand and to determine the location of the image, its orientation, size, and the type of image formed. However, the ray diagrams do not give us the numerical details such as how far the image is located from the object etc. In order to find the numerical details we use the Mirror Formula. Mirror Formula: 1/f = 1/do + 1/di Here f = focal length do = object distance di = image distance Sign Convention: f = positive, if the mirror is a concave mirror (it is negative if it is a convex mirror). di = positive, if it is a real image located on the same side as the object. di = negative, if it is a virtual image and is located behind the mirror. Magnification formula: The ratio of the height of the image and the height of the object is equal to the ratio of the image distance and the object distance. This equation is known as the Magnification equation. Magnification, M = hi/ ho = - di/do Here, hi = image height ho = object height di = image distance do = object distance Sign Convention: hi = positive, if the image is upright (this also implies that the image in the concave mirror is virtual) hi = negative, if the image is inverted (this also implies that the image in the concave mirror is real) Example: A 3.00cm tall lamp is placed at a distance of 26.4cm from the concave mirror. The concave mirror has a focal length of 15.00cm. Determine the image distance and the size of the image. Given information: ho = 3.00cm do = 26.4cm f = 15cm If the focal length of the concave mirror is 15cm, then it implies that the center of curvature which is double the focal length is at 30cm. From the given object distance and focal length, we can observe that the object is actually placed in between the center of curvature and the focal point. Applying the Mirror Formula we have: 1/f = 1/do + 1/di 1/15 = 1/26.4 + 1/di This implies: 1/di = 1/15 1/26.4 Taking the common denominator we get: 1/di = (26.4 15)/ 396 1/di = 11.4/396 So, di = 396/26.4 == di = 34.7cm (approximately) This implies that the image distance is 34.7cm Now, to find the image size we use the Magnification equation Magnification, M = hi/ ho = - di/do This implies: hi/ 3.00 = - 34.7/ 26.4 hi = - 3.94cm (approximately) Therefore the size of the image is - 3.94cm (negative value implies that the image is inverted). Magnification, M = hi/ ho Hence, M = 3.94/ 3 = 1.31 (nearly) Now, from the calculated image distance, di we can observe that the location of the image is far beyond the center of curvature and this fits in perfectly well with our above mentioned Location 3 - the object located in between the center of curvature and the focal point. Also, we can observe that the image formed is magnified and since it is inverted it is also a real image!