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.

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Date

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Principal

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Teacher-in-charge

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External Examiner

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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

1. 2. 3. 4.

Contents

Page No.

Introduction

5

Aim and Apparatus required

6

Theory

7

Procedure

11

Precautions and Sources of error

17

Result and uses

18

7.

Bibliography

19

8.

Photo Gallery

20

5. 6.

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INTRODUCTION

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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EXPERIMENT

To determine the focal length of convex lenses by the following methods: (i) The plane mirror method (ii) The displacement method

Convex lenses of various focal lengths, plane mirror, optic bench, light source, lens holders.

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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

2

and hence f = [d

– a2]

/4d 8

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: 2

2

d ( u + v ) / d u = [ u - 2u f] / [ u – f ]

For a minimum,

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d (u + v) d u = 0 ,

u

2

– 2 u f = 0.

or

Therefore:

2

u = 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 11

TABULATION - 1 S.no.

Position of mirror (cm)

Position of convex lens (cm)

) Position of object pin ( cm)

Focal length (cm)

Mean focal length (cm)

1.

2.

3.

4.

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





Focal length (cm)


1.

2.

3.

4.


12





Focal length (cm)


1.

2.

3.

4.






Focal length (cm)


1.

2.

3.

4.


13

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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Distance between object and image a (cm)

First position of lens (d1)

Second position of lens (d2)

Lens displacement d = d1 d2 –

Mean focal length (cm) 2

[d

– a2] /4d

1.

2.

3.

4.


TABULATION -2 S.no.






[d

– a2] /4d

1.

2.

3.

4.


15







[d

– a2] /4d

1.

2.

3.

4.








[d

– a2] /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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Object distance (U) cm

Image distance (V) cm

U+V

1

2

3

4





U+V

1

2

3

4

RESULT: Focal length of the given Convex lens ___________ cm. 18




U+V

1

2

3

4


TABULATION – 4 S.no.



U+V

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-convexlens/



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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