First slide

Coherent sources and their importance in interference

Question

When one of the slits in Young's experiment covered with a transparent sheet of thickness $3.6 \times 10^{- 3}$ cm the central fringe shifts to a position originally occupied by the 30th bright fringe. If $λ = 6000 Å$ , the refractive index of the sheet is

Moderate

A

1.50
B

1.55
C

1.60
D

1.65

Solution

The position of the 30th bright fringe is given by
$y_{30} = 30 \frac{λD}{d}$
Hence the shift of the central fringe is
$y_{0} = 30 \frac{λD}{d}$
$But y_{0} = \frac{D}{d} (μ - 1) t$
$\begin{array}{l} ∴ 30 \frac{λD}{d} = \frac{D}{d} (μ - 1) t \\ or (μ - 1) = \frac{30 λ}{t} = \frac{30 \times (6000 \times 10^{- 10})}{(3 .6 \times 10^{- 5})} = 0 .5 \\ ∴ μ = 1 .5 \end{array}$

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