Experiment 18C

Experiment 18C: Thin Lenses

Purpose

To measure the focal lengths of thin lenses, and to construct and test a compound lens.

Apparatus

(a) optical bench with a mounted lamp and screen

(b) a set of two lenses, one brown and one green, two lens mounts, and a desk lamp

Theory

I) A thin lens is characterized by its focal length f. The object distance s, the image distance s', and the focal length are related by the thin lens equation, Formula (1):

(1)

Using this formula, you can calculate the focal length by measuring s and s’.

II) When two thin lenses lens1 and lens2 are placed in contact with each other, the result is a compound lens. Its focal length fcomp is related to the focal lengths (flens1 and flens2) of its two components by formula (2):

fcomp = (2)

Preliminary Procedure

Make sure that:

● the centers of all lenses and the lamp are aligned along the horizontal optical axis

● the planes of all lenses are perpendicular to the optical axis

Procedure Part I: Measuring the Focal Length of the Brown Lens

(A) Place the lamp (the object) at the position x0 = 0.0 cm. It should remain there throughout all parts of the experiment. This will simplify the calculation of the object distance s. Record your sample number on your data sheet and copy the following table:

Brown Lens Data
Original Orientation / Reversed Orientation
Trial / brown lens position xbr (cm) / screen position
xscr (cm) / Trial / brown lens position xbr (cm) / screen position
xscr (cm)
1 / 5
2 / 6
3 / 7
4 / 8

lamp (object)

Figure 1 Optical Bench Setup for Part 1

B) Place the brown lens about 21-23 cm from the lamp and record its position to within 0.1cm accuracy, as xbr, of Trial #1. Place the screen beyond the lens, as shown in Figure 1, and move it back and forth until you see a focused image. Record the screen position (the image position) as xscr for Trial #1.

C) Repeat this three more times, with xbr ranging from about 19 cm to about 30cm, spaced evenly. Record xbr and the corresponding xscr for each trial.

D) Reverse the brown lens’ orientation by rotating the shaft 180º. Make four trials as before, placing the lens between 19 and 30 cm. Record xbr and the corresponding xscr for each trial.

E) Optional (consult your Instructor): Make a direct measurement of fbr by focusing a far-away object on the screen. Make two such measurements, one of them in reversed position, and find their average value.


Procedure Part II: Measuring the Focal Length of the Green Lens

(F) Prepare a similar table for the green lens on your data sheet.

(G) Place the green lens about 20-22cm from the lamp and find the focused image. Record the lens and image positions, xgr and xscr, as before under Trial #1.

(H) Repeat three more times, with xgr ranging between 18 and 28 cm, evenly spaced, and record the corresponding xscr.

(H) Reverse the green lens. Make four trials with different values of xgr and record the corresponding xscr.

(J) Optional (Consult your Instructor): Repeat (E) for the green lens.

Procedure Part III: The Compound Lens

(K) Your brown and green lenses can be combined into a compound lens. Press your lenses together as shown in Fig. 2 - it will make no difference which one of the two you will reverse. Mount them carefully in a single holder. There is no need to "paste" them together.

(L) On your data sheet, prepare a table for the compound lens as you did for the brown and green lenses. Now repeat the entire procedure: Start with the compound lens at about

10 cm and make four trials between 10 and 20 cm. Reversal the compound lens and take

4 more trials.


Lab Report

Part I: The brown lens

1) Copy Table I. Calculate s and s’ for each trial using your measurements of xbr and xscr. (See Figure 1.)

2) Calculate fbr for each trial using the Thin Lens Equation, Formula (1). Show one sample calculation including units. Display your results in Table I. Find the averages for original and reversed orientations separately. Then calculate the total average:

fbr> = (<f1> + <f2>) / 2

TABLE I. Brown Leans Results
Original Orientation / Reversed Orientation
Trial # / s / s’ / fbr / Trial # / s / s’ / fbr
1 / 5
2 / 6
3 / 7
4 / 8
AVE<f1 / AVE<f2

Question #1: If your values of <f1> and <f2> differ by more than 0.5 cm, state the likely reason.

2a) If you have done the optional item (E) (the direct measurement of fbr), find the average for both orientations and compare it with the result under (2). Comment on your result.

Part II: The green lens

Question # 2: Is Formula (1) useful for calculating fgr? Explain.

3) Write Table II similar to Table I. Calculate fgr for each trial and the averages as in (2). Display your results in Table II. Calculate <fgr>.

3a) If you have done the optional item (J), do (2a) for the green lens.

Part III: The Compound Lens

4) Construct Table III (also similar to Table I) and calculate <fcomp using Formula (2).

5) Calculate the theoretical value of the focal distance of the compound lens by Formula (2) and display the %-difference between the theoretical and experimental values using the experimental value as the denominator.

Question #3: Was it really necessary to reverse the compound lens? Explain your answer.

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