If the angle of incidence is twice the angle of refraction in a medium of refractive index μ , then the angle of incidence is

Question

If the angle of incidence is twice the angle of refraction in a medium of refractive index μ , then the angle of incidence is (A)  2 cos -1(μ /2)  (B)  2 sin -1(μ /2)  (C)  2 cos -1μ  (D)  2 sin -1μ

Tardigrade Admin · Accepted Answer

According to Snells law μ =( sin i/ sin r) i=2r μ =( sin 2r/ sin r)⇒ μ =(2 sin r cos r/ sin r) cos -1(μ /2)=r

Q. If the angle of incidence is twice the angle of refraction in a medium of refractive index $μ,$ then the angle of incidence is

$2 cos^{- 1} \frac{μ}{2}$

$2 sin^{- 1} \frac{μ}{2}$

$2 cos^{- 1} μ$

$2 sin^{- 1} μ$

According to Snells law
$μ = \frac{s i n i}{s i n r}$
$i = 2 r$
$μ = \frac{s i n 2 r}{s i n r} \Rightarrow μ = \frac{2 s i n r c o s r}{s i n r}$
$cos^{- 1} \frac{μ}{2} = r$

Q. If the angle of incidence is twice the angle of refraction in a medium of refractive index μ, then the angle of incidence is

2cos−12μ​

2sin−12μ​

2cos−1μ

2sin−1μ