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Q.

In Young’s double slit experiment, the fringes are displaced by a distance x when a glass plate of refractive index 1.5 is introduced in the path of one of the beams. When this plate is replaced by another plate of the same thickness, the shift of fringes is $(3 / 2) x .$ . The refractive index of the second plate is

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a

1.50

b

1.25

c

1.75

d

1.00

answer is A.

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Detailed Solution

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Fringe shift is given by $x = \frac{(μ - 1) t β}{λ}$
For first plate, $x = \frac{(μ_{1} - 1) t β}{λ}$
For second plate, $\frac{3}{2} x = \frac{(μ_{2} - 1) tβ}{λ}$
$\begin{array}{l} \Rightarrow (\frac{μ_{2} - 1}{μ_{1} - 1}) = \frac{3}{2} \Rightarrow (\frac{μ_{2} - 1}{1.5 - 1}) = \frac{3}{2} \\ \Rightarrow μ_{2} = 1.75 \end{array}$

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