Question

Light is incident at an angle of 30 degrees and 45 degrees on the same face of the given rectangular slab. If the angles of refraction, at this face are r1 and r2 in the two cases. Obtain the relation between two angles.

Answer 1

We know that refractive index of an object can be expressed in sin of angle i / sin of angle r
i.e. sin i / sin r = constant ...(1)
This will be true for all values of i and r.
Therefore we can equate the two angles.
Sin30° / SinR1 = Sin45° / SinR2
=> SinR1 / SinR2 = Sin30° / Sin45°
=> SinR1 / SinR2 = 1/2 ÷ 1/√2
=> R1/R2 = 1/√2
Or √2R1 = R2