JEE Main202122 Jul 2021Morning ShiftPhysicsRay OpticsActual
A ray of light passes from a denser medium to a rarer medium at an angle of incidence i . The reflected and refracted rays make an angle of 90 ° with each other. The angle of reflection and refraction are respectively r and r ' . The critical angle is given by,
Options
- Asin - 1 ( cot r )
- Btan - 1 ( sin i )
- Csin - 1 tanr '
- Dsin - 1 ( tan r )
Correct answer
D. sin - 1 ( tan r )
Step-by-step solution
r + r ' + 90 ° = 180 ° ⇒ r ' = 90 - r = 90 - i n 1 sin i = n 2 sin r ' = n 2 sin ( 90 - i ) n 1 sin i = n 2 cos i ⇒ tan i = n 2 n 1 Now sin C = n 2 n 1 = tan i ⇒ C = sin - 1 ( tan i ) = sin - 1 ( tan r )