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.
Ans
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.
Ans
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.
Ans
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.
Ans
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.
Ans
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
+ …