Name: Normal Incidence of Light Ray
Uploaded: 2019-07-19
Duration: 4 min 35 s
Description: When a light ray falls on a glass slab, the way it is refracted depends on the ray that is incident on the glass slab. Watch the video to learn more about it.

Question

A plane light wave with wavelength $λ = 0.70 μm$ falls normally on the base of a biprism, made of glass $(n = 1.520)$ with refracting angle $θ = 5.0 °$ . Behind the biprism there is a plane-parallel plate, with the space between them filled up with benzene $(n' = 1.500)$ . Find the width of a fringe on the screen $S c$ placed behind this system.

Accepted Answer

Using the last problem, we know that fringe $Δ x$ width in Fresnel biprism is given by,

$∆ x = \frac{(a + b)}{2 a ψ} λ$ , where symbols have their usual meaning.

First, let us calculate the value of $ψ .$ Consider the following diagram,

Let us apply Snell's law at point $A,$

$n \sin i = n' \sin r$

$\Rightarrow n sinθ = n' \sin r [∵ i = θ]$

As the angles are very small, so we have

$sinθ = θ & \sin r = r$ .

Hence, we have

$n θ = n' r$

$∴ r = \frac{n θ}{n'} . . . (1)$

Now, let us apply Snell's law at point $B .$

$∴ n' \sin (r - i) = n \sin α$

For small angles, we have

$n' (r - i) = n α$

$\Rightarrow n' r - n' θ = n α [∵ i = θ]$

$\Rightarrow n' (\frac{n θ}{n'}) - n' θ = n α$ [using equation $(1)$ ]

$\Rightarrow (n - n') θ = n α$

$∴ α = (\frac{n - n'}{n}) θ . . . (2)$

Now, let us apply Snell's law at point $C,$

$n \sin α = 1 \times \sin ψ$

For small angles, we have

$n α = ψ$

$∴ ψ = n (\frac{n - n'}{n}) θ = (n - n') θ$ [using equation $(2)$ ]

Now, let us calculate fringe width.

Since a parallel beam is incident on the prism, so the real source is located at infinity.

$∴ a \to \infty$

$∴ ∆ x = \lim_{a \to \infty} (\frac{a + b}{a}) \frac{λ}{2 ψ} \Rightarrow ∆ x = \lim_{a \to \infty} (1 + \frac{b}{a}) \frac{λ}{2 ψ} \Rightarrow ∆ x = \lim_{a \to \infty} (1 + \frac{b}{\infty}) \frac{λ}{2 ψ}$

$∴ ∆ x = \frac{λ}{2 ψ} = \frac{λ}{2 (n - n') θ}$

Substituting the values, we get

$∆ x = \frac{0.70 \times 10^{- 6}}{2 (1.520 - 1.500) \times (\frac{5}{180} \times π)}$

$\Rightarrow ∆ x = 0.20 mm$

Important Questions on OPTICS

Learn and Prepare for any exam you want !