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Q.

In Young’s double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance d $(d > > b)$ from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

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a

$λ = \frac{b^{2}}{d}$

b

$λ = \frac{2 b^{2}}{d}$

c

$λ = \frac{b^{2}}{3 d}$

d

$λ = \frac{2 b^{2}}{3 d}$

answer is A, C.

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Detailed Solution

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For dark or missing wavelength $y_{n} = \frac{(2 n - 1)}{2} \frac{dλ}{b}$
$\begin{array}{l} or \frac{b}{2} = (\frac{2 n - 1}{2}) \frac{d}{b} λ \\ or λ = \frac{b^{2}}{(2 n - 1) d} \end{array}$
For n = 1,2 $λ = \frac{b^{2}}{d}, \frac{b^{2}}{3 d} .$

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