Prove the Statement . If the Angle of Incidence and Angle of Emergence of a Light Ray Falling on a Glass Slab Are I and E Respectively, Prove That, I = E. - Science

Diagram

Prove the statement .

If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.

Advertisement Remove all ads

Solution 1

Let \[\mu\] be the refractive index of the glass slab. Then, according to Snell's law,

\[\frac{\sin i}{\sin r_1} = \mu\] .....(i)

and

\[\frac{\sin r_2}{\sin e} = \frac{1}{\mu}\] .....(ii)

But, r₁ = r₂ .....(iii)
Putting (iii) in (i), we have

\[\frac{\sin r_2}{\sin e} = \mu\] .....(iv)
Multiplying (i) and (iv), we have

\[\frac{\sin i}{\sin e} = 1\]
or
\[i = e\]

Solution 2

in figure. PQ || SR
NM is a refracted ray. ∴ 𝑟= 𝑖₁
By the laws of refraction,
_𝑔𝑛_𝑎= `(sin i)/(sin r) ; _a n_g= (sin i _1)/(sin_e)`
` therefore _g n_a = 1 / (" _a n_g) `
∴ `(sin i)/(sin r) = (sin e)/(sin i _1) .......but r=i_1`
∴ sin 𝑖 = sin 𝑒
∴ 𝑖 = 𝑒