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.

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#### 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, r

Putting (iii) in (i), we have

_{1}= r_{2}.....(iii)Putting (iii) in (i), we have

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

Multiplying (i) and (iv), we have

Multiplying (i) and (iv), we have

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

or

\[i = e\]

or

\[i = e\]

#### Solution 2

in figure. PQ || SR

NM is a refracted ray. ∴ ЁЭСЯ= ЁЭСЦ_{1}

By the laws of refraction, _{ЁЭСФ}ЁЭСЫ_{ЁЭСО}= `(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 ЁЭСЦ = sin ЁЭСТ

∴ ЁЭСЦ = ЁЭСТ

Concept: Refractive Index

Is there an error in this question or solution?

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