BS Physics (Foundation) Series

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Module # 41
Telescope, Microscope & Michelson Interferometer
Telescope
The purpose of a telescope is to see a clear and distinct image of
an object that is at a very far off distance from the observer.
Without the telescope, the visual angle of the object at the eye is
very small. To increase the visual angle of the object, a lens
(objective) of very large focal length is used. Large focal length is
used to achieve the larger linear magnification. In order to
observe finite objects such as the moon, the sun, the stars and
distant galaxies, the lens must have the ability to gather as much
light as is possible. This can be achieved by having a lens of large
diameter. Thus, the objective lens used in a telescope is of large
focal length and large diameter.
The brightness of the image depends upon the amount of light
entering the objective. Hence, the objectives of powerful
telescopes have large apertures.
There are two types of telescopes;
(i) Refracting telescope
(ii) Reflecting telescope

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In a refracting telescope, a real image of a distant object is formed
at the focus of the objective or object glass. This image is then
seen through a magnifying glass, called the eye-piece or eye-
lens. The magnifying power of big telescopes is more than 1000.
In a reflecting telescope, a concave mirror is used in place of
objective lens and a real image of a distant object is formed at the
principal focus of the concave mirror. This image is then seen
through an eye-piece.
Astronomical Telescope
It is the telescope which is used to see stars, planets and other
heavenly bodies in the sky.
Construction
An astronomical refracting telescope consists of two convex
lenses fixed at the ends of two metallic tubes. One of these tubes
can slide into the other so that the distance between the two
lenses can be changed. The objective of the telescope is a
convex lens of large focal length and large aperture while the eye-
piece is a convex lens of small focal length and small aperture.
Working
The rays from the distant object (stars) entering the objective are
almost parallel. After passing through the objective lens, these

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rays give rise to a real, inverted and diminished image 1 of the
object at the principal focus of the objective lens. The position of
eye piece lens is so adjusted that this image is also formed at the
focus of the eye piece lens. It acts as a virtual object for the eye-
piece lens which forms a virtual, erect and magnified image 2 of
the real image formed by the objective lens. This image is virtual
with respect to the real image but inverted with respect to the
object. For greater magnification, the objective lens should be of
large focal length and eye piece lens should be of smaller focal
length. We know that the virtual image cannot be obtained on the
screen behind the eye-piece lens. If the distance between the two
lenses is made slightly greater than the sum of focal lengths of
the lenses, then, instead of virtual image, a real image is obtained
on the screen and distant object can be photographed. No longer
does an astronomer spend much time looking through a
telescope with his eyes. Instead, a camera is attached to the
telescope to take photographs of distant objects.
The Yerkes refracting telescope is the largest of its kind in the
world. The diameter of its objective lens is about one meter. The
telescope is about 18 m long and is located at William Bay, Lake
Geneva, Wisconsin.

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Fig: Outer View & Formation of Image with an Astronomical
Telescope
Heavenly Bodies
Heavenly bodies are all spherical; therefore, their inverted images
as seen through an astronomical telescope have no
disadvantage.
Galilean Telescope or Galileo’s Telescope
It consists of an objective which is a convex lens of large focal
length and large aperture (diameter) and an eye-piece which is a
concave lens of smaller focal length and smaller aperture
(diameter). The eye-piece is fitted in a small tube which can slide
inside a bigger tube so that the distance between the two lenses
can be altered (changed). The real, inverted and diminished
image A1B1 is formed by the objective. The eye-piece E is
interposed and the final virtual, magnified and erect image A2B2 is
formed as shown in the figure below.

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Fig: Galileo’s Telescope
When A1B1 is at focus of eye-piece, then, final erect image A2B2 is
formed at infinity. At this position,
length of telescope = distance between lenses
= fo - fe
= difference in focal lengths.
where fo is the focal length of the objective and fe that of the eye-
piece. The final image formed by it is erect. The length is also
small as compared to the terrestrial telescope and hence this can
be used in the construction of binoculars. The magnifying power
of a Galilean telescope is M = fo/fe.

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Advantages and Disadvantages of the Galilean or Galileo’s
Telescope
(a) Advantages
(1) The final image is erect.
(2) The telescope has shorter length than that of astronomical
telescope and terrestrial telescope.
(3) It is used to see terrestrial objects.
(b) Disadvantages
(1) It has a small field of view.
(2) It is impossible to place the eye in such a position that it
collects all the light which has passed through the objective lens.
(3) In an astronomical telescope, cross-wire is placed at the
position of the intermediate image. No such cross-wire is used in
Galilean telescope; therefore, the Galilean telescope cannot
measure precisely the angular position of the object.
(4) Its magnifying power is comparatively small.
Comparison between Astronomical and Galilean Telescopes
Points of Similarity

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(1) Both the telescopes are refracting telescopes i.e. both have
two lenses one of which is the objective and the other an eye-
piece.
(2) The focal length of the objective in both of them is greater
than that of the eye-piece.
(3) Both the telescopes are used to see distant objects.
(4) In both the telescopes, the objective is a convex lens of large
foal length and large aperture (diameter).
(5) When focussed for parallel rays, the magnifying power in
both is fo/fe.
Points of Dissimilarity
(1) In an astronomical telescope, the eye-piece is a convex lens
while in the Galilean telescope it is a concave lens.
(2) The astronomical telescope forms an inverted image and is
usually used to view heavenly bodies, whereas, the Galilean
telescope forms an erect image and is used for viewing terrestrial
objects, which is an advantage in favor of the Galilean telescope.
(3) The astronomical telescope is longer in length (size) than the
Galilean telescope. For normal adjustment, the length of the
astronomical telescope is fo + fe while, in the latter case, the

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length is fo - fe. This is again an advantage of the Galilean
telescope.
(4) The magnifying power and the field of view of the
astronomical telescope is greater than that of the Galilean
telescope.
(5) In the case of an astronomical telescope, the cross wire or a
scale can be placed at the common focal plane of the objective
and the eye-piece for measurements, whereas, no such
arrangement is possible in the case of Galilean telescope.
Terrestrial Telescope
An astronomical telescope is used only to see the heavenly
objects like stars and planets, because their inverted images do
not make any difference as they are spherical. When the distant
objects on the earth are seen through the telescope, it is desirable
to see the final image erect.
This can be achieved by placing a third convex lens between the
objective lens and the eyepiece.
Thus, in this connection, terrestrial telescope is a telescope used
to see the objects on earth in erect form. It is basically an
astronomical telescope, but, it has an additional lens L placed
between the objective lens Lo and the eye-piece Le. The function

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of L is to erect the image; therefore, it is called erecting lens (or
field lens). The image A'B' formed by the objective is real, inverted
and smaller (or diminished) in size w.r.t the object AB. The lens L
of focal length F is placed at distance 2F from image A'B' so that
the erect image A"B" may be formed on other side of L at
distance 2F. Then, eye-piece Le is so adjusted that A" A"B" lies
within its focus and final virtual, erect and very large image AB
is formed in front of the eye-piece as shown in the figure below.
That is, the image A"B" serves as object for eye-piece and final
image is observed as A'"B'" which is also erect w.r.t. object. Due
to addition of field lens (or erecting lens), the length of terrestrial
telescope is considerably increased.
Fig: Terrestrial telescope. The lens in between the objective and
the eye-piece erects the image.
Compound Microscope
It is an instrument which helps to see the magnified images of
very small objects, e.g., germs, bacteria, etc.

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Construction
It consists of two convex lenses fixed at the ends of two tubes.
One of the tubes can move into the other so that the distance
between the lenses can be changed. The lens near the eye is
known as eye piece and the lens near the object to be examined
is called objective. The focal length of objective is much smaller
than that of eyepiece. In most compound microscopes, two or
more objective lenses of different focal lengths are mounted on a
rotating disc, called the nosepiece. One objective lens is used at a
time.
Working
The object is placed slightly away from the principal focus F of the
objective. The distance of the object from the objective can be
changed as required. The objective forms a magnified, inverted
and real image 1 within the focal length of eyepiece. Eyepiece
thus forms a magnified, virtual and inverted image with respect to
the actual object.
This image is 2. To get an erect image, we place the object
inverted in front of the objective. To get different magnifications,
we use objectives of different focal lengths.

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Fig: External View of a Compound Microscope
Fig: Formation of Image in a Compound Microscope
Simple Microscope or Magnifying Glass
A simple convex lens held close to the eye can be used as a
simple microscope to magnify the image. Thus, a magnifying
glass or a reading glass is simply a single bi-convex (converging)
lens of a short focal length. The object to be seen as magnified is
placed within the focal length of the lens. This produces an
enlarged, virtual and erect image towards the object itself.
If an object AB is placed at a distance p, less than the focal length
of the lens L, then, a virtual, erect and magnified image A'B' of
this object is obtained on the same side, at least distance d of
distinct vision from the eye.

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Fig: While using a magnifying glass, the eye is focussed on the
image 25 cm from it. The actual object is much close to the eye
and so the angle subtended by it is much larger.
The magnification of a magnifying glass is given by
M = 1 + d/f
Where, f is the focal length of the lens and d is the near point
distance of the object which is about 25 cm for the normal human
eye. We can find the near point distance d for our eyes by seeing
how close we can hold a page and still read it easily.
Now, let us calculate (determine) the magnifying power as given
above.
Magnifying power of a simple microscope is given as
M = i /o ______ [1]

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Where, i is the angle subtended at eye by the image and o is
the angle subtended at the unaided eye by the object.
Now, by trigonometry, from above figure [a & b] we have
tano = AB/d and tani = A'B'/d
But, when the angle is small, then,
tano = o
and
tani = i
So,
o = AB/d
and
i = A'B'/d
By putting these values in eq. [1], we get
M = A'B'/AB = q/p = d/p _____ [2]
Now, by using the lens equation,
1/q + 1/p = 1/f
we get
-1/d + 1/p = 1/f

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(Here q = -d because the image is virtual)
OR
-1 + d/p = d/f
OR
d/p = 1 + d/f
[i.e. by multiplying both sides by d]
But
M = d/p
by eq. [2] above
Hence,
M = 1 + d/f
Uses
A simple microscope is used by
(1) Astrologers to read fate-lines of the hand,
(2) Biology students to see slides,
(3) Watch repairers to locate defects, and
(4) Detective (investigation) department to match finger prints.

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Difference between a Telescope and a Microscope
Sr.
No.
Telescope Microscope
1 It is used for seeing distant
objects.
It is used for seeing very small
objects lying very close to the
objective.
2 It has an objective of large
aperture.
It has an objective of small
aperture.
3 It has an objective of long
focal length.
It has a small objective of
short focal length.
4 It has a small eyepiece of
short focal length.
It has a large eyepiece of
large focal length.
Michelson (1852-1931)
The interferometer invented by an American physicist A.A.
Michelson is an ingenious device which splits a light beam into
two parts and then recombines them to form an interference
pattern after they have travelled over different paths. The device
can be used for obtaining accurate measurements of wavelength
and for precise length measurements.

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During the classical physics period (1700-1890 AD), several
physicists determined the velocity of light but the present
accepted value was found by Michelson.
Michelson Interferometer
The interferometer invented by an American Physicist, A. A.
Michelson was named as Michelson Interferometer. It is an
instrument which is used for the accurate measurement of wave
lengths and precise length measurements.
Its working principle is based on interference. When a light beam
falls upon it, then, it splits the light beam into two parts and
thereafter recombines them to produce an interference pattern
after they have travelled over different paths.
Fig: Michelson Interferometer
M2
Fixed
MirrorM

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A schematic diagram of the interferometer is shown in the above
figure. A beam of light provided by a monochromatic source ‘A’ is
split into two rays by a partially silvered mirror M inclined at 45°
relative to the incident light beam. One ray (i.e. ray No.2) is
reflected vertically upward towards mirror M1 while the other ray
(i.e. ray No.1) is transmitted horizontally through M towards mirror
M2. Hence, the two rays travel separate paths ℓ1 and ℓ2.
After reflecting from mirrors M1 and M2 the two rays eventually
recombine to produce an interference pattern, which can be
viewed through a telescope.
The reflected ray (i.e. ray No.2) passes more than once through
mirror M while the transmitted ray (i.e. ray No.1) passes once only
before interfering. Therefore, a glass plate D, equal in thickness to
M, is placed in the path of transmitted ray (i.e. ray No.1) in order
to equalize the path length of the two rays. With this arrangement,
each ray will then pass through the same thickness of glass.
The path difference is varied by moving mirror M1 parallel to itself
with a finely threaded screw. If a dark fringe appears at the centre
of the interference pattern, then, the two rays interfere
destructively. If M1 is moved through a distance of /4, then, the
reflected ray (i.e. ray No.2) will travel this distance twice, once on

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the onward journey towards M1 and second on backward journey
from M1. Thus, a path difference changes by,
/4 + /4 = /2
The two rays will now interfere constructively, giving a bright
fringe.
If now the mirror M1 is moved through an additional distance /4
(total distance moved in two attempts = /4 + /4 = /2), then, the
path difference changes by ‘’ (i.e. /2 + /2 =) and a dark fringe
will appear. Thus, we see that successive dark and bright fringes
are formed each time when M1 is moved a distance /4.
We thus conclude that if we have a dark fringe in the beginning,
then, the next dark fringe will appear by moving M1 to a distance
/2 (i.e. by moving M1 two times through /4) every time. If ‘m'
number of fringes pass through a reference point when the mirror
M1 is moved a distance p, then;
P = m (/2) = ½ m
OR
 = 2p/m

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This equation shows that just by counting the number of fringes
and by measuring the distance p through which mirror is moved,
the wave length '' of light can be measured.
Since the interferometer can accurately measure displacement,
so, it is often used to make highly precise measurements. The
fundamental definition of the meter is based on a certain
wavelength of light from krypton-86. The interferometer is used to
calibrate meter in terms of wavelength of light emitted by krypton-
86.