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

Question

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

Tardigrade Admin · Accepted Answer

According to Snell's law Refractive index, μ=( sin i/ sin r) Given, i = 2r ∴ μ=( sin 2r/ sin r) or μ=(2 sin rcos r/ sin r) or cos-1 (μ/2)= r ⇒ i = 2 cos-1(μ/2)

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

$2 co s^{- 1} \frac{μ}{2}$

$2 s i n^{- 1} \frac{μ}{2}$

$2 co s^{- 1} μ$

$2 s i n^{- 1} μ$

According to Snell's law
Refractive index, $μ = \frac{s i n i}{s i n r}$
Given, $i = 2 r$
$∴ μ = \frac{s i n 2 r}{s i n r}$
or $μ = \frac{2 s i n rcos r}{s i n r}$
or $cos^{- 1} \frac{μ}{2} = r$
$\Rightarrow i = 2 cos^{- 1} \frac{μ}{2}$

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

2cos−12μ​

2sin−12μ​

2cos−1μ

2sin−1μ