First slide

Young's double slit Experiment

Question

In two separate set-ups of the Young's double slit experiment, fringes of equal width are observed when lights of wavelengths in the ratio 1 : 2 are used. If the ratio of the slit separation in the two cases is 2 : 1, the ratio of the distances between the plane of the slits and the screen in the two set-ups is

Easy

A

4 : 1
B

1 : 1
C

1 : 4
D

2 : 1

Solution

As $β = \frac{Dλ}{d} \Rightarrow \frac{β_{1}}{β_{2}} = (\frac{D_{1}}{D_{2}}) (\frac{λ_{1}}{λ_{2}}) (\frac{d_{2}}{d_{1}})$
$\Rightarrow 1 = (\frac{D_{1}}{D_{2}}) \times (\frac{1}{2}) \times (\frac{1}{2}) \Rightarrow \frac{D_{1}}{D_{2}} = \frac{4}{1}$

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