A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index √2 . The angle of deviation of the ray is:

The correct option is C 15°

​​​​​​​Now see in ​triangle ADE,

• ∠EAD + ∠ADE + ∠DEA = 180°

∠ADE = 180° - (∠EAD + ∠DEA)

∠ADE = 180° - (30° + 90°)

∠ADE = 180° - 120°

∠ADE = 60°

• Now see,

• r2 + ∠ADE = 90°

r2 = 90° - ∠ADE

r2 = 90° - 60°

r2 = 30°

• Now using Snell’s law,

• µglass (Sin r2 ) = µair (Sin e)

• Now putting the values,

• (Sin e) = µglass/air (Sin r2 )

Sin e = √2 (Sin 30°)

Sin e = √2 (1/2)

Sin e = 1/√2

• Sin e = Sin 45°

• e = 45°

• As we have already studied the relation,

• i + e = A + ẟ

• ẟ = (i + e) - A

ẟ = (0° + 45°) - 30°

ẟ = 45° - 30°

• ẟ = 15°

• Therefore the angle of deviation is 15°