1. Reflection is governed by the equation –i = –r¢ and refraction by the
Snell’s law, sini/sinr = n, where the incident ray, reflected ray, refracted
ray and normal lie in the same plane. Angles of incidence, reflection
and refraction are i, r ¢ and r, respectively.
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2. The critical angle of incidence i
c
for a ray incident from a denser to rarer
medium, is that angle for which the angle of refraction is 90°. For
i > i
c
, total internal reflection occurs. Multiple internal reflections in
diamond (i
c
@ 24.4°), totally reflecting prisms and mirage, are some
examples of total internal reflection. Optical fibres consist of glass
fibres coated with a thin layer of material of lower refractive index.
Light incident at an angle at one end comes out at the other, after
multiple internal reflections, even if the fibre is bent.
FIGURE 9.26 Schematic diagram of a reflecting telescope (Cassegrain).
the telescope tube. One must have an eyepiece and the observer right
there, obstructing some light (depending on the size of the observer cage).
This is what is done in the very large 200 inch (~5.08 m) diameters, Mt.
Palomar telescope, California. The viewer sits near the focal point of the
mirror, in a small cage. Another solution to the problem is to deflect the
light being focussed by another mirror. One such arrangement using a
convex secondary mirror to focus the incident light, which now passes
through a hole in the objective primary mirror, is shown in Fig. 9.26.
This is known as a Cassegrain telescope, after its inventor. It has the
advantages of a large focal length in a short telescope. The largest telescope
in India is in Kavalur, Tamil Nadu. It is a 2.34 m diameter reflecting
telescope (Cassegrain). It was ground, polished, set up, and is being used
by the Indian Institute of Astrophysics, Bangalore. The largest reflecting
telescopes in the world are the pair of Keck telescopes in Hawaii, USA,
with a reflector of 10 metre in diameter.
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3. Cartesian sign convention: Distances measured in the same direction
as the incident light are positive; those measured in the opposite
direction are negative. All distances are measured from the pole/optic
centre of the mirror/lens on the principal axis. The heights measured
upwards above x-axis and normal to the principal axis of the mirror/
lens are taken as positive. The heights measured downwards are taken
as negative.
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4. Mirror equation:
1 1 1
v u f
+ =
where u and v are object and image distances, respectively and f is the
focal length of the mirror. f is (approximately) half the radius of
curvature R. f is negative for concave mirror; f is positive for a convex
mirror.
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5. For a prism of the angle A, of refractive index n2
placed in a medium
of refractive index n1
,
n
n
n
A D
A
m
21
2
1
2
2
= =
( ) +
( )
sin /
sin /
where Dm
is the angle of minimum deviation.
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6. For refraction through a spherical interface (from medium 1 to 2 of
refractive index n1
and n2
, respectively)
n n n n 2 1 2 1
v u R
−
− =
Thin lens formula
1 1 1
v u f
− =
Lens maker’s formula
1 2 1 1 1
1 1 2 f
n n
n R R
=
( − )
−
R1
and R2
are the radii of curvature of the lens surfaces. f is positive
for a converging lens; f is negative for a diverging lens. The power of a
lens P = 1/f.
The SI unit for power of a lens is dioptre (D): 1 D = 1 m–1
.
If several thin lenses of focal length f
1
, f
2
, f
3
,.. are in contact, the
effective focal length of their combination, is given by
1 2 3
1 1 1 1
f f f f
= + + + …
The total power of a combination of several lenses is
P = P1
+ P2
+ P3
+ …
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7. Dispersion is the splitting of light into its constituent colour.
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8. Magnifying power m of a simple microscope is given by m = 1 + (D/f),
where D = 25 cm is the least distance of distinct vision and f is the
focal length of the convex lens. If the image is at infinity, m = D/f. For
a compound microscope, the magnifying power is given by m = me
× m0
where me
= 1 + (D/f
e
), is the magnification due to the eyepiece and mo
is the magnification produced by the objective. Approximately,
o e
L D
m
f f
= ×
where f
o
and f
e
are the focal lengths of the objective and eyepiece,
respectively, and L is the distance between their focal points.
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9. Magnifying power m of a telescope is the ratio of the angle b subtended
at the eye by the image to the angle a subtended at the eye by the
object.
o
e
f
m
f
β
α
= =
where f
0
and f
e
are the focal lengths of the objective and eyepiece,
respectively.
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1. The laws of reflection and refraction are true for all surfaces and
pairs of media at the point of the incidence.
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2. The real image of an object placed between f and 2f from a convex lens
can be seen on a screen placed at the image location. If the screen is
removed, is the image still there? This question puzzles many, because
it is difficult to reconcile ourselves with an image suspended in air
without a screen. But the image does exist. Rays from a given point
on the object are converging to an image point in space and diverging
away. The screen simply diffuses these rays, some of which reach our
eye and we see the image. This can be seen by the images formed in
air during a laser show.
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3. Image formation needs regular reflection/refraction. In principle, all
rays from a given point should reach the same image point. This is
why you do not see your image by an irregular reflecting object, say
the page of a book.
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4. Thick lenses give coloured images due to dispersion. The variety in
colour of objects we see around us is due to the constituent colours
of the light incident on them. A monochromatic light may produce an
entirely different perception about the colours on an object as seen in
white light.
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5. For a simple microscope, the angular size of the object equals the
angular size of the image. Yet it offers magnification because we can
keep the small object much closer to the eye than 25 cm and hence
have it subtend a large angle. The image is at 25 cm which we can see.
Without the microscope, you would need to keep the small object at
25 cm which would subtend a very small angle.
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