Experiment 18U

Experiment 18U: Thin Lens Equation

Purpose

(1)To observe images formed by lenses; to practice focusing.

(2)To measure the focal lengths of lenses, using the Thin Lens Equation.

Apparatus

(a) Optical bench, with mounted lamp and screen.

(b) A set of 3 lenses, color-tagged RED, YELLOW, and BLUE; two lens mounts.

(c) A desk lamp.

Theory

A thinlens is characterized by its focal length f. The object distance S, the image distance S´, and the focal length are related by (1), the Thin Lens Equation. Equation (1) can be used for all kinds of thin lenses, provided the following sign-conventions are observed. / (1) / BASIC EQUATION
+ =

(i) fis positive for converging lenses, negative for diverging lenses.

(ii) S is positive if the object is in front of the lens, according to the direction of lightrays. But if the object is behind the lens ( = virtual object) then S is negative.

(iii) S´ is positive if the image is behind the lens, and negative if it is in front of the lens ( = virtual image).

Formula (1) and the sign conventions can be used for a succession of lenses, with the principle: the image formed by a preceding lens (according to the direction of light rays!) serves as an object for the following lens.

Preliminary Procedure

Familiarize yourself with the Optical Bench. Your instructor should explain the details to you.

At all times during the experiment, make sure that:

(i) The centers of all lenses and the center of the lamp are aligned along a (horizontal) optical axis.

(ii) The planes of all lenses are perpendicular to the optical axis; the same applies to the screen and the lamp.

Procedure Part I: Measuring f of a Converging Lens

(a) Place the lamp (the primary object) at the position xo= 0.0 c,; it should remain there through all parts of the experiment.

Record your sample-number on your data-sheet. Use only the lenses belonging to your sample

.

(b) Prepare a table on your data-sheet as shown in Fig.1.

RED LENS DATA /
RUN # / RED LENS
POSITION
XR (cm) / SCREEN
POSITION
XSCR (cm) / FOCAL
LENGTH
fR ( cm)
1
2
3
4
5
6
7
8
AVERAGE < fR

(c) Place the RED lens about 12 to 13cm from the lamp and record its position, within

1 millimeter accuracy, as xR, under Run #1. Then place the screen behind the lens and move it back-and-forth until you observe the image to be sharp and undistorted; this process is known as focusing.

(CALL YOUR INSTRUCTOR IF IN DOUBT)

(d) Repeat (c) for additional seven runs (for a total of 8 runs) with xR ranging from 11 to 25 cm, evenly spaced. Record xR and xSCR in the table.

(e) From the Basic Equation (1) and the particular
situation in Fig. 1, one can derive a “Handy Formula” (2). Use it to complete, on your data-sheet, the Red Lens Table; calculate the average value < fR >. / (2) / HANDY FORMULA
(Valid Only for Fig.1)
fR = ( xSCR – xR ) xR
xSCR

(f) Optional (consult your Instructor): Make a direct measurement of fR by focusing a far-away object onto the screen.

DO NOT PROCEED FURTHER UNTIL YOUR INSTRUCTOR CHECKS AND APPROVES YOUR RESULTS.

Procedure Part II: Image Formed by Two Converging Lenses

(g) Place the RED lens at twice its focal length from the lamp; clamp it securely and record its position as xR. Locate the image (using the screen) and record its position as xKEY.

During the remainder of the experiment the position of this image (xKEY) shall not be changed.

(h) Remove the screen. Keep in mind that the image is still there, at xKEY. Place the YELLOW lens about 10 to 12cm beyond xKEY.

The image at xKEY now serves as the object for the YELLOW lens.

Place the screen beyond the YELLOW lens and locate the new image, as sharp andundistortedas possible. On your data-sheet, prepare a table:

YELLOW LENS DATA:
Original
YELLOW
LENS
Position / Run # / xY(cm) / xSCR (cm) / REVERSED
YELLOW
LENS
Position / Run # / xY(cm) / xSCR (cm)
1 / 4
2 / 5
3 / 6

Record the position xY of the YELLOW lens and of the image xSCR under

Run #1. Repeat, by moving the YELLOW lens back-and-forth, and re-focusing the image, for a total of 3 runs.

(i) Reverse the yellow lens in its holder, make additional three runs and record all data. (The reason for reversing is that the center of the YELLOW lens does not

exactlycorrespond to the plane of the lens-holder).

(j) Optional (Consult your Instructor): Make a direct measurement of fY by focusing a far-away object onto the screen. Make sure you make two such measurements, one of

them in reversed position. Calculate the average value.

Procedure Part III: The Diverging Lens

(k) Make sure that your RED lens is still in the same position as in Part II, so that there

is still an image at xKEY, which will againserve as your object. Mount the Blue lens and make sure it is properly aligned. Place theBLUE lens about 6 or 7cm in front of xKEY position. Next, move the screen and locate the image as sharp and undistortedas possible (usually, this will be possible only for the central portion of the image). On your data-sheet, prepare a table similar to that for the yellow lens. Part II (h). Make and record three runs in original and three more in reversed mounting.

Lab Report

Part I

1) Calculate fR.

2) Show, by algebra, why the formula (2) follows from the equation (1), for the situation in Fig. 1.

3) If you have done the focusing of a far-away object onto the screen, display the

%-discrepancy between <fR> from (e)from (f).

Part II

4) Draw a diagram of your experimental set-up, similar to Fig. 1, showing clearly all five positions:

xo , xR , xKEY ,xY, xSCR

Display the formulae from which you will calculate S and S΄ for the YELLOW lens in terms of xY , xKEY, and xSCR.

5) Copy and complete the table below:

CALCULATION of fY (FOCAL LENGTH OF YELLOW LENS)
Original
YELLOW
LENS
Position / Run # / S / S΄ / fY / REVERSED
YELLOW
LENS
Position / Run
# / S / S΄ / fY
1 / 4
2 / 5
3 / 6
AVE: / AVE:
OVERALL AVERAGE < f Y > =

6)(i) Comment on the discrepancies between the values of fY in individual runs. If they are large, figure out the reason.

(ii) Comment on the difference between the averages for the original and the reversed mountings of the lens.

Part III

7) Draw a diagram of your experimental set-up, similar to Fig. 1, showing clearly all five positions:

xo , xR , xKEY , xB, xSCR

Display the formulae from which you will calculate S and S´ for the BLUE lens, in terms of xB, xKEY, and xSCR.

8) Set up and complete a table, using the +/- sign convention, similar to that for the yellow lens (in Part II above).

9) Comment on all discrepancies and figure out the reasons for them.

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