1220PHYS Lenses Students Lab Manual 2010(b)

8/3/2019 1220PHYS Lenses Students Lab Manual 2010(b)

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Student Name: __________________ Partners: _____________________________

Student Number: __________________

Day and Time: __________________

Date: ________

Week: ________

LABORATORY 4

OPTICAL LENSES

Specific Safety Precautions Optical Lenses Experiment

Below is a list of risks and controls specific to this experiment. Please read it carefully beforecommencing the experiment and refer to it as necessary during the course of the experiment.

Further details can be found in the Standard Operating Procedure and Risk Assessment

document for this experiment, which is available in the laboratory.

Risk ControlEye damage due to focused light. Do not stare into focused beam.

Burns received from hot incandescent lamp

bulb and housing.

Be aware of and do not touch hot surfaces

on lamp and lamp housing.

Exposure to dangerous voltages from faulty

equipment.

Do not use faulty equipment.

Report faulty equipment to demonstratorimmediately.

Check all power cords for visible

deterioration prior to use.

Trip hazard due to obstructions in

walkways

Keep bags under benches to avoid

obstructions.

PHYS 1220 Labor at ory


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INTRODUCTION

Figure 1. Ray diagram for a simple converging lens.

A typical thin lens consists of glass or plastic that has been ground so its two surfaces are

segments of spheres. They are commonly used to form images by refraction in cameras,

telescopes, microscopes and other optical instruments. Figure 1 shows the ray diagram for

locating the image of an object a distance s from a thin converging lens. The image distance

s'is related to s and the lens focal length,f by

fss

1

'

11=+ . (1)

When s + s' > 4f, the lens can be moved to two positions to form an image for the same value

of s + s'. These are known as conjugate positions and are illustrated in Figure 2.

Figure 2. Conjugate positions of a converging

lens.

In this situation, the lens forms an image at an object: image distance, L for two different

object distances s1 and s2.


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OBJECTIVES- To study the formation of images by convex and concave lenses.

- To determine the focal lengths of convex and concave lenses.

KEY WORDSConvex and concave lenses, focus, focal length, image, object

REFERENCESD.C. Giancoli, Physics for Scientists and Engineers with Modern Physics, 3

rded., Prentice

Hall, New York, 2000.

APPARATUSOptical bench Light source

Convex lens on stand Concave lens on stand

Ground glass screen on stand Slide with arrow

Metre stick Trammel bar

Spherometer

PREPARATION (Homework)(a) Read the sections of the text that discuss images formed by convex and concave thin

lenses.

(b)Draw labeled ray diagrams, illustrating the formation of images for each of the

following cases. Show ray directions on all diagrams. For all cases,f=10 cm.


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(i) Converging lens with s = 4f

(ii) Converging lens with s = 0.5f

(iii) Diverging lens with s = 2f


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YOUR WORK IN THE LABORATORY

Part I: Focal length of a converging lens.

Approximate Focal Length

(i) Hold a sheet of paper as a screen to view the image formed by the lens of a distantobject (e.g. a window). Obtain an approximate value of the focal length of the lens. If

the object distance, s is large, then s'=fand the image is formed at a distance from the

lens equal to the focal length (see equation 1).

The approximate value of the focal length:

Optical Bench Determination of Focal Length.

(ii) Place the light source near one end of the optical bench with the slide (object) close tothe light. Using the approximate value just obtained forf, place the lens approximately

4ffrom the object. Place the screen on the other side of the lens and with the light

source switched on to illuminate the object, move the screen along the optical bench

to obtain the sharpest, focused image of the object. When the image is located,

carefully measure and record s and s' in Table 1.

s (m) s(m) f (m) f (m)

MPE

Table 1. Measurements for the converging lens

(iii) Leave the object and image positions as found in (ii) fixed and by moving the

lens, locate the conjugate lens position where a sharp image is again obtained on the

screen. Measure and record s and s'. Starting with a different object-image distance

repeat (ii) to (iii) inclusive above. This should give a total of 4 values forf.


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(iii) Calculate f(equation 1) and f(equation 2)for each position

(iv) All the values offshould agree to within about 10%. If they don't, consult ademonstrator. Calculate and record the average focal length.

Average focal length:

(v) Errors for quantities can be calculated in two ways, either by using the MPE obtainedfrom multiple measurements as above, or by calculating the error from the errors

in a single measurement. Use the first approach by calculating the maximum

deviation of your experimental focal lengths from the average focal length.


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Part II: Focal length of diverging lens using a virtual object.

The focal length of a diverging lens can be determined from the lens equation if a

virtual object is used. The setup is shown in Figure 3 and the procedure is as follows:

(i) Position the converging (convex) lens ~25cm cm from the object and move the screen

so that a sharp image of the object is formed (at D in Figure 3). Record the position of

the lens and the screen. This image will serve as a virtual object for the diverging

(concave) lens (C).

Figure 3. Arrangement for determining the focal length of a diverging lens.

(ii) Place the diverging lens on the optical bench as shown in Figure 3 making |s2 |

approximately 0.75 s1 '. What is the sign of s2 (positive or negative)?

(iii) Move the image screen to locate the focused image and record s2 ', together with

uncertainties for s2 and s2 '. The uncertainty for s2' is set by the error in s1 plus the

error in measuring s2. The error in s2' is obtained by noting the range over which the

image remains sharp.

(iv) Calculatef2, the focal length of the diverging lens, from s2 and s2' and equation (1).


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(v) Calculate the uncertainty inf2 from

2

2

2

2

1

1

f

f

f

f

=

(2)

+

=

222'

111

ssf(3)


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Part III: Determination of the converging lens focal length using a spherometer

(i) The focal length of a thin symmetrical lens is given by1/f = (n-1) 2/R , (4)

where n is the refractive index and R is the radius of curvature of the glass.

(ii)Use the spherometer to measure the radius of curvature of the lens as shown inAppendix A. If n=1.5 for the glass, calculatefand compare with your

experimental value above.

APPENDIX A(i) The spherometer has 3 fixed legs and a centre leg which can be moved by turning a

screw. The distance, h, through which the centre leg moves is shown on main and

circular scales.

(ii) Check the zero error of the instrument by noting the scale reading when all four legs

touch a plane surface. Record your measurement of the zero point then adjust the

centre leg so all legs touch the surface of the lens. For d, the distance between two ofthe fixed legs, the radius of curvature is given by

h

dh

2

3R

22 +

= . (5)


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APPENDIX B

Derivation of expression for error in focal length

'

111

ssf+=

+

=

'

111

ssf

Fractional errors ins

1and

'

1

s

s

s

s

s =

1

1

so2

1

s

s

s

=

and'

'

'

1

'

1

s

s

s

s =

so2'

'

'

1

s

s

s

=

Fractional error inf

1

f

f

f

f =

1

1

so f = 21

ff

Substitute for

f

1from Eq (3)

f = 2

'

11f

ss

+

Substitute for

s

1and

'

1

sfrom Eqns (4) and (5)

f = 222 '

'f

s

s

s

s

+


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Final Report

Based on your experimental data write a brief (~2 page) report in the following format:

Title

Name Partners

Date Lab No. Week

Use the following headings in your report:

Abstract

(Present BRIEFLY: what you have done and what have you obtained)

Experimental Procedure

(Short (may be dot-point) instruction-like description of how to carry out the experiment andwhat to measure)

Final Results

(Present BRIEFLY final results (quantitative and qualitative) of your measurements with

errors)

Discussion and Conclusions

(Do your measurement agree with the expected value of the measured quantities?)

Comment on the errors; which ones are the greatest and how they might be reduced)

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Documents

1220PHYS Lenses Students Lab Manual 2010(b)