Back To CoursePhysics: High School
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David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.
A lens is a transmissive optical device that affects the focusing of a light beam through refraction. To modify an image, light must be focused at a point where your eye can view it. Refraction is the bending of light when it moves from one medium to another. This is the process by which lenses work - they bend light until the image appears as we want it to, whether further away, closer, inverted, sharper...you name it.
We can use lenses to observe the largest things in the universe with a telescope and some of the smallest things with a microscope. And, they've given sight to people who could hardly see at all.
Lenses work according to their shape. And there are two main shapes we need to consider. Convex lenses are lenses that converge light, bending light that is spreading apart until the beams come together to meet at a point. And concave lenses are lenses that diverge light, bending light that's coming together to make the beams spread further apart. The exact properties of a lens tell you what it will do.
We can analyze what a lens will do in a number of ways. We could plug numbers into equations and do it mathematically. But in today's lesson, we're going to talk about another method - drawing ray diagrams.
A ray is a path of light drawn as a straight line coming from a source. It's a way of illustrating the direction light is moving and is much simpler than drawing the complex waves that make it up. By drawing rays and following some basic rules, we can figure out what image will be produced by a lens. The rules are slightly different for a concave versus a convex lens.
Step 1: Draw your principal axis - just a horizontal line on your paper. Draw your lens in the middle of that line. And draw two dots on each side of the lens, at the same distance away from it, and mark them F for focal point. If you wanted to draw the diagram to scale, you might actually find out the official focal length of the lens you're using, and position the focal length appropriately. A focal length of 30 centimeters might become 3 centimeters on your diagram, depending on how large your piece of paper is. This first step is the same, regardless of the type of lens. Although convex and concave lenses might look different, the important part of drawing them in terms of the diagram is just the flat line right down the middle of the lens. Drawing the shape of the lens is mostly for show and as a reminder.
Step 2: Draw your object. We usually draw this as a stick-figure stood on the principal axis, or even just an upright arrow. You might have to place the object inside the focal point, at the focal point, or outside the focal point depending on the the question.
The next few steps are for a CONVEX lens:
Step 3: Draw a straight line from the top of your object through the nearest focal point. Once the ray hits the lens, bend the line parallel to the principal axis.
Step 4: Draw a second straight line from the top of your object parallel to the principal axis. Once the ray hits the lens, bend it so that it goes through the focal point on the far side of the lens.
But what if the lens is concave? For a concave lens, steps 3 and 4 are slightly different.
For a CONCAVE lens:
Step 3: Draw a straight line from the top of your object towards the focal point on the far side. But once the ray hits the lens, bend the line parallel to the principal axis (so the ray never actually reaches the focal point it was pointed towards).
Step 4: Draw a straight line from the top of your object parallel to the principal axis. Once the ray hits the lens, bend it so that it goes directly away from the focal point on the near side of the lens.
Now let's continue with step 5 for both types of lenses.
Step 5: Regardless of the type of lens, draw a third straight line from the top of your object through the point where the principal axis meets the lens itself. This line doesn't need to bend; it just continues completely straight all the way across the paper.
Step 6: Where the three lines meet is where the top of your image is formed. The bottom of your image is always formed on the principal axis. For a concave lens, the three lines actually don't meet. They spread apart. But you can trace them backwards with dotted lines until they meet on the same side of the lens as the object.
Step 7: Study the position where the three rays meet, and use this to draw a new stick-figure or arrow that represents the image. If the three rays meet below the principal axis, then the image must be inverted, or upside down. Or, if the three rays meet far above the height of the object, then the image must be larger than the original object.
You can also figure out if the image is 'real' or 'virtual'. A real image is one where you can project it on a piece of paper, and therefore, it forms on the opposite side of the lens to the object. A virtual image, on the other hand, forms on the same side of the lens as the object. That makes it impossible to project it onto a piece of paper. Your piece of paper would get in the way of the light from the object.
Step 8: Ask yourself: is the image smaller, larger, or the same size? Is it upright or inverted? And, is it real or virtual? Note down your answers. Answering those three questions describe your image fully, and this is your ultimate goal in drawing a ray diagram.
To practice these steps, complete these tables: one for convex lenses, the other for concave lenses. Place the object at different positions, draw a ray diagram, and see what the image is like.
Here are some example ray diagrams. All of these were created using the same three rays I just described. The only difference between the concave and convex lens diagrams is which focal point you use for each step. The three rays are fundamentally the same: a parallel ray that bounces through the focal point, a ray towards the focal point that bounces parallel, and a ray going right through the center of the lens.
At this point, if you haven't already, stop reading and get started drawing some ray diagrams and completing your table.
Okay, so now you're done. Here's what you should have come up with. If these tables differ from your answers, go through the steps carefully and see where you went wrong. It's possible your lines just weren't straight enough or that your focal points weren't equal distances from the lens. This has to be done very carefully.
Eyeglasses are the most common everyday example of lenses. They work by taking the light from an object your eyes can't focus on properly and turning it into an image at a distance your eyes can handle.
A near-sighted person is someone who cannot properly focus on distant objects. Corrective glasses for nearsightedness focus the light to create an image closer to the person's eye so that they can see it. This is done using a concave lens.
A far-sighted person is someone who cannot properly focus on nearby objects. Corrective glasses for farsightedness focus the light further away from the person's eye so they can see it. This is done using a convex lens.
A lens is a transmissive optical device that affects the focusing of a light beam through refraction. To modify an image, light must be focused at a point where your eye can view it. Refraction is the bending of light when it moves from one medium to another. This is the process by which lenses work.
Lenses work according to their shape, and there are two main shapes we need to consider: convex and concave. Convex lenses are lenses that converge light, bending light that's spreading apart until the beams come together to meet at a point. And, concave lenses are lenses that diverge light, bending light that would otherwise be coming together to make the beams spread apart more. The exact properties of a lens tell you what it will do. We can analyze what a lens will do by drawing a ray diagram. To do this, you just follow the steps outlined in today's lab.
After concluding this lesson, you should now be able to:
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Back To CoursePhysics: High School
18 chapters | 212 lessons