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LENSES IN COMBINATION

OBJECTIVES

1. To determine the focal length of a diverging lens by using it in combination with a converging lens; 2. To construct a basic compound microscope.

THEORY

Diverging lens Refraction at the surfaces of a diverging lens causes the parallel rays to diverge, giving rise to a virtual image . This is defined as the point from which the diverging rays appear to come, as shown in Figure 1. The lens equation from the previous lab (TL) still applies; however the focal length of a diverging lens is negative.

1 1 1p q f+ = (1)

where p is the object distance, q is the image distance, and f is the focal length of the lens. The uncertainty in the focal length is also calculated in the same way as in the previous lab:

2

22

qppqqpf

)( +Δ+Δ

=Δ (2)

Recall that if p and/or q are negative, the negative sign(s) must be used in the denominator of this expression. Compound microscope A compound microscope consists of a short focal length objective lens which is slightly more than one focal length from the object to be viewed, and an eye lens which is slightly less than one focal length from the image produced by the objective lens. The magnification of each lens is given by

m qp

=− (3)

The overall magnification of the microscope is the product of the magnifications of each of the lenses alone.

Figure 1. Virtual mage formed by a diverging lens

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If the focal length of a lens is known and an image at a particular magnification is desired, the necessary image and object distances can be found from the equations given above. From Equation 3, q = -mp. Substituting this expression for q into Equation 1 and solving for p gives

p f mm

=−⎛

⎝⎜⎞⎠⎟

1 (4)

APPARATUS

Optical bench set: base, 2 supports, illuminated object, 2 lens holders, screen holder, ground glass screen, 3 biconvex lenses (5, 10, 20 cm) circular diaphragm stops, desk lamp.

PROCEDURE, ANALYSIS AND RESULTS

Part A - Focal lengths Assemble the optical bench. Find the approximate focal length of each of the converging lenses by locating the image of a distant object, as done in the previous experiment (TL). Record your data in the normal way. Part B – Focal length of a diverging lens It is difficult to use parallax to locate the virtual image formed by a diverging lens, because the image always appears between the object and lens, so a pointer at the image location blocks the light rays that form the image. An alternative way to find the focal length of a diverging lens is to use it in combination with a converging lens to produce a real image, as shown in Figure 2. First, an object (labelled OC) is placed in front of the converging lens alone. The converging lens forms a real image (labelled IC). Then, the diverging lens is inserted between the converging lens and IC. The diverging lens causes the final real image (ID) to move further back and become larger. The image IC acts as a virtual object (OD) for the diverging lens. Note that pD < 0. By measuring the positions of the diverging lens, IC, and ID, it is possible to calculate pD and qD, and hence find fD. 1. Put the object near one end of the optical bench. Place the long focal length converging lens

at a distance approximately equal to 2fC from the object. Locate the real image IC, and record its position. Do not move the object or the converging lens in the steps that follow.

2. The uncertainty in fD will be small when the distance between ID and IC is large. Set the final image location ID by moving the screen 30 to 40 cm back from its location at IC. This is where the final image will eventually appear. (Note that if you move the screen too far back, it will be more difficult to focus the highly magnified image, and this increases the uncertainty in fD.)

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Figure 2. Real image formed by converging/diverging lens combination 3. Insert the diverging lens between the converging lens and IC. Leaving the screen fixed at the

location in step 2, move the diverging lens until a magnified, real, inverted image (ID) is f focused on the screen. Record the positions of the screen and the diverging lens. Carefully estimate the uncertainty in the diverging lens position based on how much you can move the lens and keep the image in focus.

4. Calculate the image and object distances for the diverging lens (see Figure 2). Use these

values in the lens equation to find the diverging lens focal length. Also calculate the uncertainty in the focal length. Remember that the object distance is negative in these calculations.

5. Draw a ray diagram, to scale, for a diverging lens with p = ─f.

Part C - Compound microscope 1. Place the illuminated object on the left end of the base and record its position. The short focal length lens will be the objective lens of your microscope. Calculate the object distance required so that an image of the object will be formed on the screen with a magnification of -4X. Calculate the lens position and place the lens on the base. No uncertainties are required in this calculation. Experimentally find the screen position which provides the best focus image. Important

• The centre of the objective lens will be offset somewhat from the pointer due to the thickness of the lens. Make sure that the centre of the lens, not the pointer, is at the proper position.

• The image position given by theory is not the actual image position due mainly to errors in your focal length measurement.

Record the lens and screen positions. 2. Mount the medium focal length (eye) lens near the end of the bench, beyond the screen. Calculate the distance that the eye lens needs to be away from the screen (this image is the object for the eye lens) in order to produce a 2X virtual image. Again, no uncertainties are

pD (< 0)

ID

OC

IC = OD

qD

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required in this calculation. Place the eye lens at this distance from the screen. Record the position of the eye lens. Mount one of the smaller diaphragms on the objective lens in order to reduce the brightness and improve the quality of the image. Remove the screen and observe the image through the eye lens. If you have difficulty finding the image, try this technique. Hold a piece of paper perpendicular to the optic axis about where your eye was. Move it toward and away from the eye lens until a small bright circle of light is seen on the paper. This is the “exit pupil” of the microscope, and is the place where the pupil of your eye should be when you look through the lens. When you are satisfied with your microscope, ask your instructor to inspect it. 3. Tidy the apparatus. 4. On a full page in your notebook, draw a scale ray diagram of your microscope. When drawing the diagram you must assume that the focal lengths of the two lenses are as found in Part A. The distances of the objects from the lenses must be as calculated in this part to achieve the -4X and 2X magnifications. Calculate the overall magnification from your ray diagram, that is, the ratio of the size of the final image to that of the object. Does it agree quite well with the design value of -8X? Hints

• The image produced by the objective lens becomes the object for the eye lens. • Start with an object which is small enough so the final image will fit on the page.