Question

A ray of light entering from air to glass ( RI = 1.5 ) is partly reflected and partly refracted .If incident and the reflected rays are at right angle to each other , then angle of refraction is

Answer 1

Since the reflected ray and incident ray are at right angles, 2 (angle of reflection)= 90⁰ ⇒ the angle of incidence = 45⁰
 Applying Snell's law,
1 x sin (45⁰) = 1.5 x sin (θ)                    (θ = angle of refraction)
1/√2 = 3/2 x sin (θ)
θ = 28.125⁰

Answer 2

Answer:

The angle of refraction is sin⁻¹ √2/3 .

Explanation:

Snell's law of reflection :

• The angle of incidence is equal to angle of reflection.
• ∠i = ∠r'
• The incident ray reflected ray and the normal at the point of incidence all lie in the same plane

Snell's law of refraction :

• The incident ray, the refracted ray and the normal to the interface at the point of incidence all lie in the same plane.
• The ratio of the sine of angle of incidence and the sine of angle of refraction is constant for a given pair of medium.
• Mathematically,
• μ = sin i/ sin r

Given that :

• Incident and reflected ray are at right angle to each other
• Refractive index of glass with respect to air is 1.5

Solution :

• Let, the incidence angle be i; reflected angle be r' and refracted angle be r.
• Since, incident ray and reflected ray are at right angle to each other
• ∠i + ∠r' = 90⁰
• But, ∠i = ∠r' ( from law of reflection )
• This gives, ∠i = 45⁰
• The refractive index of glass is 1.5 .
• 1.5 = sin 45⁰/ sin r

⇒ sin r = √2/3 .

⇒r = sin⁻¹ √2/3 ·