Today we will see how to make project on 'project on Topic : To Determine The Combined Focal Length Of The Lens' this project is only for class 12th student and this project is belongs to 'OPTICS' in this project we will cover following steps
1. Aim
2. Introduction
3. Requirements
4. Procedure
5. Observations
6. Calculations
7. Precautions
8. Sources Of Errors
9. Bibliography
10. Conclusion
AIM
To determine the combined focal length
of one Concave and one convex lenses separated by a finite distance.
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
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
|
APPLICATIONS OF COMBINATION OF CONVEX AND CONCAVE LENS
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.
REQUIREMENTS
1.
An optical bench with three uprights (central
upright fixed, two outer uprights with lateral movement)
2.
One convex lens
3.
One Concave lens
4.
Two lens holder
3.
Two optical needles
6. Half metre scale
PROCEDURE
vTake one
concave and convex lens.
v Find the rough
focal length of the two lenses L1(convex) and L2(concave) individually having
focus length of f1 and f2 respectively.
v Keep the lenses
in front of the window and obtain a sharp image of the object placed at
infinity.
v Measure the
distance between lenses and the image formed with the help of scale.
v Now find the
accurate focal length of two lenses L1 and L2 by using the experimental setup
individually and calculate its focal length reading.
v 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.
v Mount the thick
optical needle in the fourth upright near the other end of the optical bench.
v 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.
v Move the eye
towards right. The tips will get separated. The image tip and the image needle
have parallax.
v Remove the
parallax tip to tip as described.
v 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
|
2.
|
Concave(L2)
|
8
|
18
|
-9
|
The separation between the two convex lenses
= 7.2 cm
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
Ø
Tips of the object and image needles should lie
at the same height as the centre of the lens.
Ø
Parallax should be removed from tip to tip by
keeping eye at a distance at least 30cm away from the needle.
Ø
The object needle should be placed at such a
distance that only real, inverted image of it is formed.
Sources of error
ü
The uprights may not be the vertical.
ü
Parallax removal may not be perfect.
BIBLOGRAPHY
1. Comprehensive
Pratical Physics Class XII
2. NCERT
Physics Part – II
3. Experimental
Physics
CONCLUSION
1.
The combined focal length of one convex and one concave
lenses having focal length 10 cm and 9 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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