A ray of light passes from the vacuum into a medium of refractive index 'n'. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

Step-by-step solution

Let the angle of incidence be i and the angle of refraction be r . Given that the angle of incidence is twice the angle of refraction: i = 2r According to Snell's law: (i) = n (r) Substituting i = 2r into the equation: (2r) = n (r) Using the double angle formula (2r) = 2 (r) (r) : 2 (r) (r) = n (r) Assuming r 0 , dividing both sides by (r) gives: 2 (r) = n (r) = n 2 r = ⁻¹ ( n 2 ) Since the angle of incidence is i = 2r , we get: i = 2 ⁻¹ ( n 2 ) Answer: 2 ⁻¹ ( n 2 )