First slide

Coherent sources and their importance in interference

Question

White light may be considered to be a mixture of wave with $λ$ ranging between $3900 \overset{0}{A}$ and $7800 \overset{0}{A}$ . An oil film of thickness $10, 000 \overset{0}{A}$ is examined normally by reflected light. If $μ = 1.4$ , then the film appears bright for

Moderate

A

$4308 \overset{0}{A}, 5091 \overset{0}{A}, 6222 \overset{0}{A}$
B

$4000 \overset{0}{A}, 5091 \overset{0}{A}, 5600 \overset{0}{A}$
C

$4667 \overset{0}{A}, 6222 \overset{0}{A}, 7000 \overset{0}{A}$
D

$4000 \overset{0}{A}, 4667 \overset{0}{A}, 5600 \overset{0}{A}, 7000 \overset{0}{A}$

Solution

The film appears bright when the path difference $(2 μ t \cos r)$ is equal to odd multiple of $λ / 2.$
$i . e ., 2 μ t \cos r = (2 n - 1) \frac{λ}{2} w h e r e n = 1, 2, 3 \dots ∴ λ = \frac{4 μ t \cos r}{(2 n - 1)} = \frac{4 \times 1.4 \times 10, 000 \times 10^{- 10} \times \cos 0}{(2 n - 1)} = \frac{56000}{(2 n - 1)} \overset{0}{A} \{F o r n o r m a l i n c i d e n c e r = 0^{o}\} \Rightarrow λ = 56000 \overset{0}{A}, 18666 \overset{0}{A}, 11200 \overset{0}{A}, 8000 \overset{0}{A}, 6222 \overset{0}{A}, 5091 \overset{0}{A}, 4308 \overset{0}{A}, 3733 \overset{0}{A} . T h e w a v e l e n g t h s w h i c h a r e n o t w i t h i n s p e c i f i e d r a n g e a r e t o b e r e f r a c t e d .$

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