This document describes a physics experiment to determine the combined focal length of one convex and one concave lens. The student measures the individual focal lengths of the convex and concave lenses and then combines them, varying their separation. Applying the lens combination formula, the student calculates the combined focal length as 14.516 cm, demonstrating that the effective focal length and power change when lenses are combined.

1. Physics
INVESTAGATORY PROJECT
Submitted By : Vikash Prasad
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XII – A
Roll No. :
Year : 2012 – 2013
Topic : To Determine The Combined Focal Length Of The Lens System
School : Kendriya Vidyalaya No.2
CERTIFICATE

2. This is hereby to certify that the project “To Determine The
Combined Focal Length Of The Lens System” is an original
and genuine investigation work carried out to investigate about
the subject matter and the related data collection and
investigation has been completed solely, sincerely and
satisfactorily by, VIKASH PRASAD of class XII – A as per the
requirement for the CBSE Board Examination for the year 2012
– 13.
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Roll No. :
Date :
Concerned Teacher Signature : Examiner Signature :
Principal Signature : School Stamp :

3. ACKNOWLEDGEMENT
I wish to express my deep gratitude and sincere thanks to
our chemistry teacher -------------- for her invaluable guidance,
constant encouragement, constructive comments,
sympathetic attitude and immense motivation, which has
sustained my efforts at all stages of this project work. Her
valuable advice and suggestions for the corrections,
modifications and improvement did enhance the perfection
in performing my job well.
I would like to express my gratitude for our honorable
principal ------------------------ for whole hearted co-operation and
guidance. I am also thankful for her encouragement and
for all the facilities that she provided for this project work. I
sincerely appreciate this magnanimity by taking me into
her fold for which I shall remain indebted to her.
I take special pleasure in acknowledging our lab assistant ---
----------- for his willingness in providing us with necessary
lab equipments and constant support without which this
effort would have been worthless.
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4. 4
Vikash Prasad
Table of content
 Aim
 Introduction
 Requirements
 Procedure
 Observations
 Calculations
 Precautions
 Sources Of Errors
 Bibliography

5. 5
 Conclusion
AIM
To determine the combined focal length of one Concave and one convex lenses
separated by a finite distance

6. INTRODUCTION
Many Optical tasks require several lenses in order to achieve an
acceptable level of performance. One such possible approach to lens
combination is to consider each image formed by each lens as the object
for the next lens and so on. This is a valid approach, but it is time
consuming and unnecessary.
In various optical instruments, two or more lenses are combined to
1. Increase the magnification of the image,
2. Make the final image erect w.r.t the object,
3. Reduce certain aberrations.
It is much simpler to calculate the effective (combined) focal length and
principal point locations and then use the results in any subsequent
paraxial calculations. Two thin lenses of focal length f1 and f2
respectively which are in closed contact, then the effective focal length
of the combination will be given by
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1/F= 1/f1 + 1/f2
And the total magnification of the lens combination will be given by
M = m1 * m2
If the lenses of focal length are separated by a finite distance d, the focal
length F of the equivalent lens is given by
1/F= 1/f1 + 1/f2 - d/f1.f2

7. APPLICATIONS OF COMBINATION OF CONVEX AND CONCAVE LENS
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1. CHROMATIC ABBERATION
One common lens aberration is chromatic aberration. Ordinary light is a
mixture of light of many different colours, i.e. wavelengths. Because the
refractive index of glass to light differs according to its colour or wavelength,
the position in which the image is formed differs according to colour, creating
a blurring of colours. This chromatic aberration can be cancelled out by
combining convex and concave lenses of different refractive indices.
2. TELEPHOTO LENSES
Most optical devices make use of not just one lens, but of a combination of
convex and concave lenses. For example, combining a single convex lens
with a single concave lens enables distant objects to be seen in more detail.
This is because the light condensed by the convex lens is once more
refracted into parallel light by the concave lens. This arrangement made
possible the Galilean telescope, named after its 17th century inventor,
Galileo.
Adding a second convex lens to this combination produces a simple
telephoto lens, with the front convex and concave lens serving to magnify
the image, while the rear convex lens condenses it. Adding a further two
pairs of convex/concave lenses and a mechanism for adjusting the distance
between the single convex and concave lenses enables the modification of
magnification over a continuous range. This is how zoom lenses work.

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REQUIREMENTS
 An optical bench with three uprights (central upright fixed, two
outer uprights with lateral movement)
 One convex lens
 One Concave lens
 Two lens holder
 Two optical needles
 Half metre scale

9. PROCEDURE
 Take one concave and convex lens.
 Find the rough focal length of the two lenses L1(convex) and
L2(concave) individually having focus length of f1 and f2 respectively.
 Keep the lenses in front of the window and obtain a sharp image of the
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object placed at infinity.

10.  Measure the distance between lenses and the image formed with the
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help of scale.
 Now find the accurate focal length of two lenses L1 and L2 by using the
experimental setup individually and calculate its focal length reading.
 With left eye closed, see with the right open eye from the other end of
the optical bench. An inverted & enlarged image of the object needle
will be seen. Tip of the image must lie in the middle of the lenses.
 Mount the thick optical needle in the fourth upright near the other end
of the optical bench.
 Adjust the height of the object needle so that its tip is seen in line with
the tip of the image when seen with the right open eye.
 Move the eye towards right. The tips will get separated. The image tip
and the image needle have parallax.
 Remove the parallax tip to tip as described.
 Combine the two lenses together with the help of two lens holder and
find its accurate combine focal length.
OBSERVATIONS
Serial
no.
Lenses Rough
focal
length(cm)
Radius of
curvature(R)
f=R/2
(cm)
1. Convex(L1) 9.5 20 10

11. 2. Concave(L2) 8 18 -9
The separation between the two convex lenses = 7.2 cm
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CALCULATIONS
1/F = 1/f1 + 1/f2 - d/f1f2
1/F = 1/10 + 1/(-9) - 7.2/(10)(-9)
1/F = -1/90 + 7.2/90 = 6.2/90
F = 90/6.2 cm
Therefore, F = 14.516 cm
PRECAUTIONS
 Tips of the object and image needles should lie at the same height
as the centre of the lens.
 Parallax should be removed from tip to tip by keeping eye at a
distance at least 30cm away from the needle.

12.  The object needle should be placed at such a distance that only real,
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inverted image of it is formed.
SOURCES OF ERROR
 The uprights may not be the vertical.
 Parallax removal may not be perfect.
BIBLOGRAPHY
 Comprehensive Pratical Physics Class XII
 NCERT Physics Part – II
 Experimental Physics
 www.wikipedia.com
CONCLUSION
1. The combined focal length of one convex and one
concave lenses having focal length 10 cm and 9

13. cm respectively and separated by a distance of 7.2
cm is 14.516 cm.
2. So on combination of the one convex and one
concave lens the effective focal length increases
and hence its effective power decreases.
3. The effective nature of the combined lens system
is converging i.e. convex lens since focal length
for the system comes out to be positive.
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