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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, r1 = r2 .....(iii)
Putting (iii) in (i), we have
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= ЁЭСЦ1
By the laws of refraction,
ЁЭСФЁЭСЫЁЭСО= `(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
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