First slide

Coherent sources and their importance in interference

Question

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 in replaced by another plate of the same thickness, the shift of fringes is (3/2)x. The refractive index of the second plate is

Moderate

A

1.75
B

1.50
C

1.25
D

1.00

Solution

$S h i f t x o n t h e s c r e e n i s g i v e n b y, x = \frac{(μ - 1) t D}{d} F o r f i r s t p l a t e, x = \frac{(μ_{1} - 1) t D}{d} F o r s e c o n d p l a t e, \frac{3}{2} x = \frac{(μ_{2} - 1) t D}{d} A f t e r d i v i d i n g, \frac{(μ_{2} - 1)}{(μ_{1} - 1)} = \frac{3}{2} \Rightarrow \frac{(μ_{2} - 1)}{(1.5 - 1)} = \frac{3}{2} \Rightarrow μ_{2} = 1.75$

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