measuring focal length of convex lens

7/23/2019 measuring focal length of convex lens

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When the intention is noble, the act is also noble, whatever be the act.

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BONAFIDE

This to certify that project report titled “ECO BRICK” is a bonafide work

done by S.SRUTHI PRIYA of class XII-B of Chinmaya Vidyala in the year

2015-2016.

……………………………….. ………………………………………………

Date Teacher-in-charge

……………………………………… ………………………………………………

Principal External Examiner

……………………………………….......

School Seal



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ACKNOWLEDGEMENTS

I would like to acknowledge my sincere thanks to Mr. C Sathiyamoorthy the

principal of my school for allowing me to use the Physics Lab to perform the

experiments that made my final project practicable. I also express my sincere

gratitude to Ms Kalavathy and Ms Vijaya (Department of Physics) for their

constant guidance and motivation. I would like to thank Mr Hari Narayanan for

his immeasurable support and my teammates for their encouraging succour.



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Index

S.No Contents Page No.

1. Introduction 5

2.

Aim and Apparatus required 6

3. Theory 7

4. Procedure 11

5. Precautions and Sources of error 17

6. Result and uses 18

7. Bibliography 19

8. Photo Gallery 20



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INTRODUCTION

The measurement of the focal length of a lens

Knowledge of the focal length of a lens is vital in the construction of all optical

instruments, from spectacles to large astronomical telescopes. The focal length of an

optical system is a measure of how strongly the system converges or diverges light. For

an optical system in air, it is the distance over which initially collimated rays are brought

to a focus. A system with a shorter focal length has greater optical power than one with a

long focal length; that is, it bends the rays more sharply, bringing them to a focus in a

shorter distance.

In most photography and all telescopy, where the subject is essentially infinitely far

away, longer focal length (lower optical power) leads to higher magnification and a

narrower angle of view; conversely, shorter focal length or higher optical power is

associated with a wider angle of view. On the other hand, in applications such as

microscopy in which magnification is achieved by bringing the object close to the lens, a

shorter focal length (higher optical power) leads to higher magnification because the

subject can be brought closer to the center of projection The range of possible focal

lengths is very large, from a few milli- metres. Several simple methods are described

because they all illustrate different aspects of the lens formula.



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THEORY :

The focal length of a lens can be determined by several techniques. Some of these are less

difficult to use than others and some are more accurate. The following two subsections

are a brief description of some of the techniques.

METHOD 1: THE PLANE MIRROR METHOD:

The lens is placed on the mirror as shown in Figure 1, and the object is moved until

object and image coincide. This point is the principal focus, since light from it will

emerge parallel from the lens and so be reflected back along its original path when it

strikes the mirror. The object can be either a pin or a point source.

Since R = 2f for a lens of glass of refractive index 1.5 placed in air, the value of f can be

found.



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METHOD 2: THE DISPLACEMENT METHOD: An illuminated object is set up in front of a lens and a focused image is formed on a screen.

For a given separation of the object and screen it will be found that there are two positions where a

clearly focused image can be formed (Figure 2). By the principle or reversibility these must be

symmetrical between 0 and I.

Using the notation shown:

d = u + v and

a = v– u

Therefore

u = [d – a]/2 and

v = [d + a]/2

Substituting in the lens equation gives:

2 / [d–

a] + 2 / [d + a] = 1 and hence f = [d

2

–

a

2

] /4d



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METHOD 3: THE MINIMUM DISTANCE METHOD:

This more mathematical method derives from the fact that there is a minimum

separation for object and image for a given lens. This can be shown if u + v is plotted

against either u or v. A minimum is formed (shown by Figure 3) and this can be shown

to occur at the point where u = v = 2f and u + v = 4f, that is, the minimum separation for

object and image is 4f.

Proof:

1/u + 1/v = 1/f

Therefore:

u + v = u v / f and

v = f u / [u– f] so,

[u + v] = u / [ u–

f ]

Differentiating the last equation with respect to u gives:

d ( u + v ) / d u = [ u2

- 2u f] / [ u – f ]2

For a minimum,



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d (u + v) d u = 0 , or

u2– 2 u f = 0. Therefore:

u2

= 2 u f or

u = 2f

v = 2f and so,

u + v = 4f.



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PROCEDURE:

Determination of the focal length of a convex lens by using the Plane

Mirror method:-

1. Arrange the plane mirror, convex lens and object pin with help of holder on the optical bench as

shown in the figure and align them properly with the help of a meter scale.

2. Fix the position of the plane mirror at one end of the optical bench. Now put the convex lens at

20cm distance from the plane mirror and locate the position of image behind the convex lens in a

way to have no parallax between the images and object pin.

3. Record the position of the plane mirror, convex lens and the object pin. Keep the distance

between the plane mirror and convex lens as 30cm, 40cm… for other set of the readings

4. The distance between the convex lens and object pin is the focal length of the convex lens.

The reading for different lens is shown in the tabulation



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TABULATION - 1

RESULT: Focal length of the given Convex lens ___________ cm.

TABULATION - 2


S.no.Position of

mirror (cm)

Position ofconvex lens

(cm)

) Position of

object pin ( cm)

Focal length

(cm)

Mean focallength (cm)

1.

2.

3.

4.

S.no.Position ofmirror (cm)


(cm)

) Position ofobject pin ( cm)

Focal length(cm)


1.

2.

3.

4.



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TABULATION - 3


TABULATION - 4


S.no.Position of

mirror (cm)


(cm)

) Position of

object pin ( cm)

Focal length

(cm)


1.

2.

3.

4.

S.no.Position ofmirror (cm)


(cm)

) Position ofobject pin ( cm)

Focal length(cm)


1.

2.

3.

4.



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Determination of the focal length of a convex lens by using the

displacement method:-

1. Place the object (o) at one end of meter scale and the image screen (I) at the end so that

distance apart is about 90 cm. [The distance between the object and screen is (D)]

2. Place the lens between then and near to the object.

3. Adjust the position of the lens until MAGNIFIED IMAGE is sharply focused on the screen.

4. Record the position of the lens along scale. The distance between the lens and object is = d1.

5. Move the lens toward the screen and adjust its position one again a diminished image is

sharply in, focus on the screen.

6. Record the new position of the lens along scale. The distance between the lens and object is =

d2.

7. Repeat the observation with the distance between the object and screen (D) equal to, 100, 95,

80 cm



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TABULATION - 1


TABULATION -2


S.no.

Distance between

object and image

a (cm)

First position of

lens (d1)

Second position

of lens (d2)

Lens

displacement d =

d1 – d2


[d2 –

a2] /4d

1.

2.

3.

4.

S.no.

Distance between

object and image

a (cm)

First position of

lens (d1)

Second position

of lens (d2)

Lens

displacement d =

d1 – d2


[d2 – a

2] /4d

1.

2.

3.

4.



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TABULATION - 3


TABULATION - 4


S.no.

Distance between

object and image

a (cm)

First position of

lens (d1)

Second position

of lens (d2)

Lens

displacement d =

d1 – d2


[d2 –

a2] /4d

1.

2.

3.

4.

S.no.

Distance between

object and image

a (cm)

First position of

lens (d1)

Second position

of lens (d2)

Lens

displacement d =

d1 – d2


[d2 – a

2] /4d

1.

2.

3.

4.



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Determination of the focal length of a convex lens by the minimum

distance method:-

1. A rough value of the focal length of the lens found by focusing the light from the lab

win‐down on to a sheet of paper. This assists in the suitable positioning of the object pin.

2. The object pin O is now placed a considerable distance (up to 100 cm) from the lens, and

the position of the image located by non‐parallax using the locating pin.

3. The distance u and v of the object pin and the locating pin from the lens are recorded.

4. A series of values of v is thus obtained with the object pin approaching the lens by steps of

10 cm. At distances in the neighbourhood of twice the focal length of the lens, it is advisable

to take shorter intervals for u.

5. From the tabulated results a graph of (u + v) against u is drawn from which the focal length

of the lens is determined.



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TABULATION - 1

S.no. Object distance (U) cm Image distance (V) cm U+V

1

2

3

4


TABULATION - 2


1

2

3

4




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TABULATION - 3


1

2

3

4


TABULATION – 4


1

2

3

4




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PRECAUTIONS:

(i)The lens, source and the screen should be vertical and in a straight line.

(ii)Ensure the principle axis is parallel to the optic bench.

(iii)Take as many readings as possible to minimise error in determining the focal length.

(iv)Note the reading from the centre of the lens.

SOURCES OF ERROR:

(i)Due to spherical aberration a perfectly sharp image cannot be obtained.

(ii)Due to chromatic aberration in lens images are coloured.

(iii)The thickness of the lens is not taken into account.



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RESULT:

The focal lengths of the convex lenses were found by the different methods mentioned above.

USES OF LENS:

Medical Applications: You can also easily check whether glasses have positive or negative

lenses by looking at an object through one lens held some distance away. When you move the lens,

the object also appears to move. If it moves in the same direction as the motion of the lens, it is

negative lens; if it moves in the opposite direction, it is a positive lens. Another test is to hold the

lens over some printing. If it enlarges the printing, the lens is positive; if it makes the printing

smaller, the lens is negative. In astigmatism, the curvature of the cornea is uneven. Astigmatism

cannot be corrected by a simple positive or negative lens. A simple test for astigmatism is to look at

a pattern of radial lines. An astigmatic eye will see lines going in one direction more clearly than

lines going in other directions. Astigmatism is corrected with an asymmetric lens in which the

strength is greater in one direction than in the perpendicular.



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BIBLIOGRAPHY

http://ephy.in/displacement-method-to-determine-the-focal-length-of-a-convex-

lens/

http://www.uobabylon.edu.iq/uobcoleges/ad_downloads/5_23809_677.pdf



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measuring focal length of convex lens

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