Geometric Optics #2

Name ______

Date ______

GEOMETRIC OPTICS #2

LENSES

PRE-LAB QUESTIONS

Review this lab procedure before coming to class and then answer the following questions:

1. In activity 1-2, you will find an image using a 100mm lens and then 200mm lens. When the image is in focus, in which case will the white screen be closer to the lens? For the 100mm lens or the 200mm lens?

2. When you block off the bottom half of the lens in Activity 1-3, what do you predict will happen to the image? For example, will the bottom half disappear? The top half? Will the entire image generally darken? Support your answer.

3. How does refraction depend upon wavelength/frequency of light?

Name ______Date ______

Geometric Optics #2

LENSES

One of the most common calculations in geometric optics is the prediction of the behavior of lenses. In the lab we will continue our study of this topic by applying the laws of refraction to lenses.

INVESTIGATION 1: SOLID LENSES

Material Required:

Light source box

Optics bench

Acrylic lenses

Glass lenses

Ruler

Compass

Activity 1-1: Single Lens

1)Set up the optics source box on a piece of white paper on the table top, with the slits arranged so that five rays are pointing down the paper.

2)Place the double-convex acrylic lens also on the paper so that all five rays hit the lens and trace the outline the lens.

Question 1-1: Does this double-convex lens cause the rays to converge or diverge?

3)Place dots along the incoming light rays as they come into the lens and at the point where they cross after they have passed through the lens. Remove the lens and draw in all the rays using the ruler. Measure the distance to the focal point from the center of the lens and record it in the table below.

4)On a second sheet of paper, have another member of your lab group repeat steps (1) through (3) for the double concave lens.

Question 1-2: Does the concave lens cause the light rays to converge or diverge?

Question 1-3: Do the light rays actually pass through the focal point of the concave lens? If not, how did you measure the focal length?

Lens type / Focal length (m)
concave
convex

Activity 1-2: Lensmaker's Equation

Another way to determine the focal length of a lens is through finding the physical radius of curvature and use the Lensmaker’s Equation.

1)Place the convex lens in the middle of a piece of paper and trace one surface on a piece of paper. Draw a tangent line to the curve near the end points of this arch you have just drawn. Now draw two lines normal to those tangentspointing away from the lens, extending them until they cross. This crossing point will give you a good estimate as to the center of curvature of this arch.

2)Check your estimate of the center of curvature by placing the sharp end of a compass on that point and attempting to lightly draw an arch on top of the arch you traced from the lens. If you do not get an exact match, adjust the compass.

3)Read the radius of the lens from the compass.

4)The Lensmaker’s Equation is given as

1/f = (n - 1)(1/R1 - 1/R2)

where n is the index of refraction of the material and R1 and R2 are the

radii of curvature of either side of the lens. In our case, both of these radii are the same. Fill is the value for the radius in the table below and calculate the focal length.

lens type / R / computed f (m)
concave
convex

Question 1-4: How do your values for the predicted focal length calculated in this activity compare with the focal length you found in Activity 1-1?

Activity 1-3: Images formed by a convex lens

1)Mount the optics source box to the bracket on the optical bench with the white square (with the printed circles) toward the far end of the bench. Place the white screen near the far end of the bench. Finally, place the convex lens with the 100 mm focal length between, approximately half way between the screen and the lens.

Prediction: You will soon be sliding the white screen into a position so that the lens forms an image of the light source on it. Will the image be inverted or upright when it is formed?

2)Measure the distance between the light source and the center of the lens and predict the point where the image will be created by this lens using our standard formula

1/f = 1/di + 1/do

Focal Length / Measured d0 / Calculated di / Measured di
100mm
200mm

Table 1-1

3)Slide the white screen along the bench until you see the image of the circles on the square on the light source come sharply into focus. Measure the distance between the lens and the white screen and record it as the “measured di” in the above table

Question 1-5: How does the measured distance image compare to the focal length of the lens? Are they the same? Should they be? Why or why not?

Question 1-6: Is the image created on the white screen inverted or upright? How can you tell?

Question 1-7: Sketch a ray diagram of the situation you have currently in lab. Show at least three of the principle rays.

Question 1-8: Is the image formed on the screen real or virtual? How can you tell?

Question 1-9: Looking at the image on the white screen, do you think the value of M (the magnification) will be greater than 1 or less than 1?

4)Measure the diameter of outer circle on the surface of the light source. Using our formula for the magnification, along with the distances from table 1-1, predict the size of the image on the white screen and record it in the table below.

M = i/o = - di/do

Focal Length / Ratio di/d0 / Predicted i / Calculated i
100mm
200mm

Table 1-2

5)Measure the size of the image on the screen and record in the table.

Prediction: What if you move the light source such that it is 100mm away from the lens? Where will the image be formed?

6)Move the light source such that it is 100mm away from the center of the lens. Find the point where image is sharply formed on the white screen. If required, removed the white screen from the optical bench so you can move it more freely.

Question 1-10: Explain the results from step (6).

Extenstion 1-3: Additional Convex Lens

1)Repeat steps (1) through (5) of activity 1-2 with the 200mm focal lengh lens.

Activity 1-4: Image Formation

Prediction: What if you were to place a piece of paper across the bottom half of the lens, blocking any light from passing through it. How do you think this would effect the image on the white screen? Would the bottom half of the image be blocked off? The top half? Would the entire image get darker? Something else? Justify your answer?
Prediction: What if you were to place a piece of paper across the right half of the lens, blocking any light from passing through it. How do you think this would effect the image on the white screen? Would the right half of the image be blocked off? The left half? Would the entire image get darker? Something else? Justify your answer?

1)Test your first prediction by placing a piece of paper across the bottom half of the screen. (Note: At this point, you may wish to adjust your lens/screen setup so that the image on the white screen is relatively large. Try using the 100mm lens and moving it relatively close to the light source.)

Question 1-11: Did the image behave as you predicted? Explain the effect of blocking off the bottom half of the screen on the image.

2)Test your second prediction by placing a piece of paper across the right half of the lens.

Question 1-12: Did the image behave as you predicted? Explain the effect of blocking off the right half of the screen on the image.

Extension 1-5: Multiple lenses

1)Telescope: Remove the optical source box and bracket from the optical bench. Tighten down securely the screen at one end of the bench, the 200 mm lens next, and finally the 100 mm lens on the optical bench. Tape an object to the screen.

2)View the object provided by placing your eye near the eyepiece lens and moving the objective lens (the one nearer to the object) until you get a clear image.

3)The virtual image of the objective lens is now in the plane of the object.

4)Qualitatively, compare the size of the image formed and the size of the provided object; estimate the magnification:

Mguess =

5)The theoretical magnification for a telescope is:

Mtheory = (-di1/do1)(-di2/do2) .

Fill in data in the Table below (using your text diagram to aid you with notations) and compute the theoretical magnification of this telescope.

di1 / do1 / di2 / do2 / Mtheory

INVESTIGATION 2: LIQUID LENSES

Material Required:

Light source box

Hollow lens shaped liquid containers

Alcohol

Water

Activity 2-1: Liquid lenses in air

Prediction: What if you were shine the five narrow parallel beams from the light source through the hollow lens container when the container is filled with air? How would the light beams be effected?

1)Place the hollow lens container on a white sheet of paper and shine the five narrow beams from the light source through it.

Question 2-1: Do the right rays behave as you predicted?

Prediction: What if you filled the two chambers that form a convex lens with water? How would the five light rays behave then if they were shined through the lens container?

2)Mark the position of the hollow lens container on the piece of paper and then fill the two chambers which form a double convex lens with water. Shine the five parallel rays through the container.

Question 2-2: Does the effect of the water in the container match your prediction?

3)Mark the position of the focal point of these rays on the same sheet of paper where you marked the position of the

Activity 2-2: Air Lens in liquid

Prediction: In the activity you just completed, you made a double convex lens where the lens had a higher index of refraction than the surrounding media. How would that same double convex lens effect the light rays if it had a lower index of refraction?

1)Place the clear plastic lid of the box that held the refraction lens on a white piece of paper. Empty the water from your liquid lens container into the top and then place the completely empty lens container in the lid.

2)Once again, shine the five parallel rays through the container. (You may have to add a little water to the lid to have about 1/8” of water through out.) What do the rays do now?

3)Now fill in the chamber of the lens container that is flat on one side and concave on the other. (Now you have an “air lens” which is double convex.) Does this have any effect on the behavior of the rays?

Name ______Date ______

GEOMETRIC OPTICS #2

LENSES

HOMEWORK

1. Which of the following can effect the focal length of a convex lens

1. Material the lens is made of

1. Material surrounding the lens

1. Radius of curvature of the lens

1. Diameter of the lens

1. Size of the object being viewed

1. Distance of the object being viewed from the lens

1. Which of the following can effect the point at which an image is formed by a convex lens

1. Material the lens is made of

1. Material surrounding the lens

1. Radius of curvature of the lens

1. Diameter of the lens

1. Size of the object being viewed

1. Distance of the object being viewed from the lens

1. A beacon in a lighthouse is produce a parallel beam of light. The beacon consists of a light bulb and a converging lens. Should the light bulb be placed outside the focal point, inside the focal point or at the focal point. Explain.

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