Honors Physics - Chapter 18: Lesson 2

Chapter 18: Lesson 2

Lenses and Ray Diagrams

Chapter 18: Lesson 2 - Lenses and Ray Diagrams

Types of Lenses

A lens is made of transparent material, such as glass or plastic, with a refractive index larger than that of air.

A convex lens is a converging lens that is thicker at the center than at the edges. Convex lenses are converging because they refract parallel light rays so that they meet.

A concave lens is a diverging lens that is thinner in the middle than at the edges. Rays passing through concave lenses spread out.

Parts of a Lens

The parts of a lens are the same as parts of a mirror. The principal axis is the straight line that is perpendicular to the surface of the lens at its center that divides the lens in half. You can see the principal axis in the picture of a convex lens. The vertical axis cuts the lens in half vertically. The vertical axis is perpendicular to the principal axis.

The focal point is the location at which the rays parallel to the principal axis of a lens converge to a point. In the picture, you can locate the focal point (F). There are two focal points for a lens because light can enter the lens from either side.

Focal length of a convex lens is the distance from the focal point to the vertical axis.

The focal length is the distance from the focal point to the mirror along the principal axis. It is abbreviated with a fancy f, ƒ. The focal length depends on the shape and the refractive index of the lens material.

The local length of a concave lens is the distance from the focal point to the vertical axis. The focal length of a concave lens is negative.

Convex Lenses

The image that is beyond the focal point of a convex lens is real and inverted.

If the object were placed at a distance twice the focal length from the lens, the point 2F, then the image is also found to be at 2F. As the object comes closer to the focal point of the lens, the image moves farther away and increases in size.

If the object is brought closer to the lens, the rays do not converge on the opposite side of the lens. The image appears on the same side of the lens as the object. In this case, the image is erect, larger, and virtual.

This is a ray diagram for how a magnifying glass works. When the object is in between the focal point and the lens, the image is larger, erect, and on the same side as the object.

Concave Lenses

A concave lens causes all rays to diverge. The focal length of a concave lens is negative. The image for a concave lens is on the same side as the object, erect, smaller, and virtual.

Similarities Between Converging and Diverging Mirrors and Lenses

You can use what you learned in Chapter 17 and apply it to lenses. Converging mirrors and lenses behave the same way. A converging mirror is concave and a converging lens is convex.

Diverging mirrors and lenses also behave the same way. A diverging mirror is convex and a diverging lens is concave.

Click on the picture to take you to a handy comparison for converging and diverging mirrors and lenses.

Converging:Diverging Comparsion

Ray Diagrams for Lenses

Just like drawing ray diagrams for mirrors, ray diagrams for lenses can be drawn to determine the size and location of an image.

There are three rays that we can draw to find the image in a lens. Remember, to find the image, we just need to know where the intersection of the refracted lines are, and to do that, you just need two rays. I will show you all three rays once, then we will just look at the two rays that are the easiest to draw.

Ray Diagrams for Convex Lens

Below are all three rays that can be used to draw ray diagrams for lenses. The third ray described, the orange one below, has a few tricks that you need to draw it for various scenarios. Because you only need two rays to find the intersection, the first and second ray (the blue and green one) will be used.

Ray 1 starts from the top of the object and goes parallel to the principal axis until it reaches the vertical axis.

The ray is then refracted through the focal point on the opposite side of the object.

Ray 2 is the easiest ray to draw! Ray 2 starts at the top of the object and then goes through the center of the lens. It does not change direction.

Ray 3 starts from the top of the object and goes through the focal point on the same side of the object until it reaches the vertical axis.

The ray is then refracted through the lens parallel to the principal axis.

Where all 3 rays intersect is where the TOP of the image is. The image is drawn from the principal axis to where the refracted rays intersect.

Ray Diagrams for Concave Lens

The focal length for a concave lens is negative. This comes into play when drawing ray diagrams for concave lenses.

Ray 1 starts from the top of the object and goes parallel to the principal axis until it reaches the vertical axis.

You then will line your ruler up with the point where ray 1 hits the vertical axis and the focal point on the same side as the object, the red line. The ray will then refract through the lens along the ruler.

Ray 2 is the easiest ray to draw! Ray 2 starts at the top of the object and then goes through the center of the lens. It does not change direction.

Layering both ray 1 and ray 2 together, you can see that the two rays will not intersect. When that happens, you need to bring the blue refracted ray back on the same side of the object.

You need to line your ruler up with the point where ray 1 hits the vertical axis and the focal point on the same side as the object, the red line. You will need to draw a dotted line back on the same side as the object. This is where the ray appears to be, but is not actually there.

The point where the two refracted rays intersect is where the TOP of the image is. The image is drawn from the principal axis to where the refracted rays intersect.

Describing the Image

To describe the image, we use the acronym LOST. This is the same way that we described images in chapter 17 for mirrors.

L stands for location. This is where the image is located. We describe the image in relation to the focal point, F, and twice the focal point, 2F.

O stands for orientation. The orientation is where we see if the image is erect (right side up) or inverted (upside down) as compared to the object.

S stands for size. We describe the size of the image as compared to the size of the object. If the image is smaller than the object or if the image is larger than the object.

T stands for type. The image is either a real image or a virtual image. A real image is where the reflected rays converge. A virtual image is where the reflected rays do not converge and we have to draw dotted lines to show where the rays appear to converge.

This image (the red arrow) is between F and 2F, inverted, smaller, and real.

This image (the red arrow) is on the same side as the object, erect, smaller, and virtual.

Check Your Understanding:

Click on the down arrow when you have your answer to check to see if you are correct.

Describe the image shown in the picture. The object is between F and 2F for a convex lens.

The image is beyond 2F, inverted, larger, and real.

2. Describe the image shown for a concave lens

The image is between F and the lens, erect, smaller, and virtual.

3. Convex lenses can form what types of images?

Convex lenses form real images when the object is beyond the focal point and virtual images when the object is between the focal point and the lens.

4. Concave lenses can form what types of images?

Concave lenses are diverging and therefore form all virtual images.

Practice Drawing Ray Diagrams

Click here for the paper that I use in the video. As you watch this video, pause it and try to draw the rays and describe the image on your own.

It is important that you know how to draw the four different convex lens cases and the one concave lens case. Use the LOST acronym to help you describe the image.

These are ALL the cases for convex lenses (4 cases) and concave lenses (1 case). If you can draw these, you will be all set!

Here is a set of blank diagrams for convex and concave lenses that you can use to print off and place an object where you need to in order to complete the ray diagram assessment or just to practice! Remember, you don't have to print this, you can also draw it yourself just as well!

Remember there are more practice ray diagrams under Chapter 18 Resources. Practice the drawing and describing the image and then see if your answer matches my answer.

Before the Next Class Period

Practice these Ray Diagrams Before Class!

Click on the picture to take you to the ray diagrams that I will be going over the next time we have class. Remember, you need to try the ray diagrams on your own to see where you make your mistakes if you want to learn how to do the ray diagrams on your own.

Convex and Concave Lenses

You have finished Lesson 2!

Be sure to head over to google classroom and fill out the exit pass.

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