(a) Why are coherent sources necessary to produce a sustained interference pattern? (b) In Young's double slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen where the path difference is $\lambda$ is $K$ units. Find out the intensity of light at a point where the path difference is $\lambda/3$.

CBSE Class 12 · 2012 · Wave OpticsShort Answer

(a) Why are coherent sources necessary to produce a sustained interference pattern?
(b) In Young's double slit experiment using monochromatic light of wavelength

λ

, the intensity of light at a point on the screen where the path difference is

λ

K

units. Find out the intensity of light at a point where the path difference is

λ /3

Answer: (a) Coherent sources keep a constant phase relationship so the fringe positions stay fixed.
(b) $I = \frac{K}{4}$ .

Solution

(a) Coherent sources emit waves of the same frequency with a constant (time-independent) phase difference. Only then do the positions of constructive and destructive interference stay fixed, giving a steady (sustained) pattern. With incoherent sources the phase difference changes randomly and the pattern shifts too fast to be seen.
(b) The intensity is

I = 4 I_{0} cos^{2} \frac{ϕ}{2}

, with

ϕ = \frac{2 π}{λ} Δ x

.
For

Δ x = λ : ϕ = 2 π \Rightarrow I = 4 I_{0} cos^{2} π = 4 I_{0} = K

.
For

Δ x = \frac{λ}{3} : ϕ = \frac{2 π}{3}

I^{'} = 4 I_{0} cos^{2} \frac{π}{3} = 4 I_{0} (\frac{1}{2})^{2} = I_{0} = \frac{K}{4}

I^{'} = \frac{K}{4}

CBSE Class 12 Board · 2012 · Subjective

Practise more: all CBSE board PYQs on Wave Optics →

CBSE Class 12 · 2012 · Wave OpticsShort Answer

Solution

More board questions on Wave Optics