JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Wave Optics

In a Young's double slit experiment the ratio of the slit's width is

4 : 1

. The ratio of the intensity of maxima to minima, close to central fringe on the screen will be

(A) $(3 + 1)^{4} : 16$
(B) $25 : 9$
(C) $9 : 1$ ✓ Correct
(D) $4 : 1$

Answer: (C)

Solution

Intensity scales with slit width, so widths in the ratio

4 : 1

mean intensities in the ratio

4 : 1

and amplitudes in the ratio

2 : 1

. At a bright fringe the amplitudes add and at a dark fringe they subtract, so

\frac{I _{max}}{I _{min}} = \frac{( A _{1} + A _{2} ) ^{2}}{( A _{1} - A _{2} ) ^{2}} = \frac{( 2 + 1 ) ^{2}}{( 2 - 1 ) ^{2}} = \frac{9}{1}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option

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