JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Wave Optics

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The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is

x : 4

where x is ______.

Answer: 1

Solution

With amplitude proportional to slit width, let the two amplitudes be

A

and

3 A

. The maximum intensity is

(3 A + A)^{2} = 16 A^{2}

and the minimum is

(3 A - A)^{2} = 4 A^{2}

. Their ratio is

\frac{I _{m i n}}{I _{m a x}} = \frac{4 A ^{2}}{16 A ^{2}} = \frac{1}{4}

, which matched to

x : 4

gives

x = 1

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Integer answer

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