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Q.

A glass plate of refractive index 1.5 is coated with a thin layer of thickness t and refractive index 1.8. light of wavelength $λ$ travelling in air is incident normally on the layer. It is partly reflected at the upper and lower surfaces of the layer and the two reflected rays interfere. If $λ = 648 nm$ , then find the least value of ‘t’ for which the rays interfere constructively?

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a

30 nm

b

60 nm

c

90 nm

d

120 nm.

answer is C.

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Detailed Solution

Conducting for costructive reference
$2 μt = (2 n - 1) \frac{λ}{2} [n = 1, 2, 3, - - -] t = (2 n - 1) \frac{λ}{4 μ}$
For least value of ‘t’, $n = 1 t_{min} = [2 (1) - 1] \frac{λ}{4 μ}$
↓
$\begin{matrix} μ = 1 .8 \\ μ = 1 .5 \end{matrix}\} t$ $t_{min} = \frac{λ}{4 μ} = \frac{648 \times 10^{- 9}}{4 \times 1 .8}$
$t_{min} = 90 \times 10^{- 9} m t_{min} = 90 nm$

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