Important Questions for Class 12 Chapter 10 - Wave Optics

Important questions based on NCERT syllabus for Chapter 10 - Wave Optics:

Question-1: What is the shape of the wave front in each of the following cases:
(a) Light diverging from a point source.
(b) Light emerging out of a convex lens when a point source is placed at its focus.
(c) The portion of the wave front of light from a distant star intercepted by the Earth

Solution:
(a) Spherical
(b) Plane
(c) Plane

Question-2: In Young’s double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. What is the intensity of light at a point where path difference is λ/3?

Solution:
Suppose,
I1 = I2 = I
Phase difference = ф
Resultant intensity is given by, IR = I1 + I2 + 2 (I1 I2)1/2 cos ф
When path difference = λ, phase difference ф =
IR = I + I + 2 √(I)2 cos0o = 4I = K
When path difference = λ/3, phase difference ф =2π/3
IR’ = I + I + 2 √(I)2 cos (2π/3) = 2I + 2I (‒1/2) = K/4.

Question-3: A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.
(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

Solution:
Let, D be the distance of screen from two slits and d be the distance between two slits.
Given,
λ1 = 650 nm = 650 × 10‒9 m, λ2 = 520 nm = 520 × 10‒9 m
For 3rd bright fringe, n = 3.
x = n λ1 (D/d) = 3 × 650 [(D/d)] nm
nth fringe due to λ2 coincides with (n ‒ 1)th fringe due to λ1.
n λ2 = (n ‒ 1) λ1 ⇒ n = 5.
Least distance required, x = n λ2 (D/d) = 5 × 520 (D/d) = 2600 D/d nm.
The values of D and d are not given in the question.