Question

Please solve this question ​

Answer 1

Ray optics

given :

a ray of light passes from vaccum to medium of refractive index u.

and angle of incidence is twice of angle of refraction

so , u1 = 1 & u 2 = u

and angle of incidence=2 i

and angle of refraction = i

apply Snell law

sin2 i × 1 = sin i× u

sin 2i/sin i = u

[we know that

sin 2x = 2sinx cosx ]

therefore,

2cos i = u

cos i = u/2

$\cos {}^{ - 1} ( \frac{u}{2} ) = i$

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Answer 2

Answer:

Given:

Light travels from vacuum to medium of refractive index μ. Angle of incidence I twice the angle of refraction.

To find:

Angle of incidence.

Calculation:

Let angle of incidence be ∠i and that of refraction be ∠r

As per the question, ∠i = 2∠r

According to Snell's Law:

$1 \times \sin(i) = \mu \times \sin(r)$

$= > \sin(2r) = \mu \: \times \sin(r)$

$= > 2 \sin(r) \cos(r ) = \mu \times \sin(r)$

$= > \cos(r) = \frac{ \mu}{2}$

$= > r = {cos}^{ - 1} ( \frac{ \mu}{2} )$

Now, we know that ,

$\angle \: i = 2 \angle \: r$

$= > \angle \: i = 2 {cos}^{ - 1} ( \frac{ \mu}{2} )$

So final answer:

$\boxed{ \red { \angle \: i = 2 {cos}^{ - 1} ( \frac{ \mu}{2} )}}$