“One of the deep secrets of life is that
all that is really worth the doing is what we do for others.”

– Lewis Carroll

Today we shall
discuss a few typical multiple choice questions on physical optics:

*Questions*(1)

*and*(2)

*are based on the following statement*:

A beam of
monochromatic light having wave length

*λ*, frequency*f*and intensity*I*in air enters a glass slab of refractive index 1.5. After traveling through the slab, the beam of light emerges through the opposite face of the slab and passes through air.
(1) Inside the slab the wave length and frequency
of the light are respectively

(a) 1.5

*λ*and 1.5*f*
(b)

*λ/*1.5 and*f*
(c) 1.5

*λ*and*f*
(d)

*λ*and*f*
(e)

*λ*and 1.5*f*
The frequency of
the light is

*unchanged*where as the speed of the light is decreased within the slab. Note that the refractive index of a medium is the ratio of the speed of light in free space (or air at ordinary pressures) to the speed in the medium. Therefore, the speed of light (v) in the glass slab is given by
v

*=*c*/*1.5 where ‘c’ is the speed of light in free space (or air).
The wave length λ,
frequency f and speed v are related as

v = f λ

Or, λ = v/f

Since the speed in
glass is (1

*/*1.5) times the speed in air, the wave length in glass is (1*/*1.5) times the wave length in air [Option (b)].
(2) The energy of the
photons in glass is

(a) 1.5 times the energy in air

(b) 1

*/*1.5 times the energy in air
(c) the same as the energy in air

(d) 3 times the energy in air

(e) 1/3 times the energy in air

The energy

*E*of a photon is given by*E = hf*where

*h*is Planck’s constant and

*f*is the frequency. Since the frequency of the light is the same in both air and glass, the energy of the photons in glass is the same as the energy in air [Option (c)].

(3) White light is
passing through a transparent plastic slab. Inside the slab

(a) the green component travels with maximum speed

(b) the green component travels with minimum speed

(c) the violet component travels with maximum speed

(d) the red component travels with maximum speed

(e) all components travel with the same speed

The refractive
index of any transparent medium is maximum for light of violet colour and
minimum for light of red colour.

[This is why violet
rays are deviated most and red rays are deviated least while traveling through
a glass prism, producing dispersion of white light].

The speed of light
(v) in the plastic slab is given by

v

*=*c*/n*where ‘c’ is the speed of light in free space (or air) and*n*is the refractive inex of the slab.
Since the
refractive index is the least for light of red colour, it follows that red
component travels with maximum speed
[Option (d)].

(4) In an experiment
with Young’s double slit, a student measures the intensity of the central
maximum of the interference pattern as

*I*. If one of the slits is covered, what will be the intensity at the position of the central maximum?
(a)

*I/*2
(b)

*I/*4
(c)

*I/*(*√*2)
(d)

*I*
(e) 2

*I*
When both slits are
open, suppose the resultant amplitude (of light wave) at the position of the
central maximum is

*a*. If one of the slits is covered, the amplitude at the position of the central maximum becomes*a/*2.
Intensity is
directly proportional to the square of the amplitude. Therefore we have

*I*α

*a*

^{2}and

*I*

_{1 }α (

*a/*2)

^{2}

Therefore

*I*_{1}=*I/*4, as given in option (b).
(5) Four laser
sources produce light waves y

_{1}, y_{2}, y_{3}, and y_{4}given (with usual notations) by*y*

_{1}=

*a*sin

*ωt*

*y*

_{2}=

*a*sin 2

*ωt*

*y*

_{3}= 2

*a*sin (

*ωt*+

*φ*)

y

_{4}= 2*a*sin (3*ωt +**φ*)
Superposition of
which two waves can produce interference fringes?

(a)

*y*_{1}and*y*_{2}
(b)

*y*_{2}and*y*_{3}
(c)

*y*_{3}and*y*_{4}
(d)

*y*_{1}and*y*_{4}
(e)

*y*_{1}and*y*_{3}
Waves

*y*_{1}and*y*_{3}have the same wave length and hence they can produce interference fringes.
[The angular
frequencies of

*y*_{1}and*y*_{3}are equal].
The correct option
is (e).

You will find a few
useful multiple choice questions in this section here.