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A light wave of wavelength $λ_{0}$ propagates from point A to point B. We introduce in its path a glass plate of refractive index n and thickness l. The introduction of the plate alters the phase of the plate at B by an angle $ϕ$ . If $λ$ is the wavelength of light in the plate, then

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$Δϕ = 0$

$Δϕ = \frac{2 πl}{λ_{0}}$

$Δϕ = 2 πl (\frac{1}{λ} - \frac{1}{λ_{0}})$

$Δϕ = \frac{2 πl}{λ_{0}} (n - 1)$

answer is C.

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Detailed Solution

$O p t i c a l p a t h d i f f e r e n c e = (n - 1) l P h a s e d i f f e r e n c e = \frac{2 π}{λ_{0}} (n - 1) l$

Further, by Snell's law,

$\begin{array}{l} nλ = (1) λ_{0} \Rightarrow λ = \frac{λ_{0}}{n} \\ \Rightarrow Δϕ = \frac{2 πl}{λ_{0}} (n - 1) = \frac{2 πl}{λ_{0}} (\frac{λ_{0}}{λ} - 1) = 2 π l (\frac{1}{λ} - \frac{1}{λ_{0}}) \end{array}$

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