CBSE Class 12 · 2003 · Wave OpticsVery Short Answer

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Two slits in Young's double slit experiment are illuminated by two different lamps emitting light of the same wavelength. Will you observe the interference pattern? Justify your answer. Find the ratio of intensities at two points on a screen in Young's double slit experiment, when waves from the two slits have path difference of
(i)

0

,
(ii)

λ /4

Answer: No sustained pattern is seen (the lamps are incoherent). For a coherent pair the ratio of intensities is $2 : 1$ .

Solution

Two independent lamps emit wave trains whose phase difference fluctuates randomly and rapidly, so no stable (sustained) interference pattern can be observed.
For two coherent sources of equal intensity

I_{0}

the resultant intensity is

I = 4 I_{0} cos^{2} \frac{ϕ}{2}, ϕ = \frac{2 π}{λ} Δ x

(i) For

Δ x = 0 : ϕ = 0 \Rightarrow I_{1} = 4 I_{0}

.
(ii) For

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

\frac{I _{1}}{I _{2}} = \frac{4 I _{0}}{2 I _{0}} = 2 : 1

CBSE Class 12 Board · 2003 · Subjective

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CBSE Class 12 · 2003 · Wave OpticsVery Short Answer

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