Question

73.A prism of critical angle 45° is
immersed in water of critical angel 50°.
The critical angle of prism inside water will
be (sin 70º = 0.94)
1) 70° 2) 90° 3) 130° 4) 100°

Answer 1

Given : prism of critical angle 45° is

immersed in water of critical angel 50°.

To find : The critical angle of prism inside water.

solution : we know,

critical angle , C = sin¯¹(1/μ)

⇒sinC = 1/μ

⇒μ = 1/sinC = 1/sin45° = √2

Therefore refractive index of glass of prism is √2

now, refractive index of glass w.r.t water,

μ₁ = μ_glass/μ_water

= √2/(4/3)

= 3/2√2

now, using formula of critical angle,

SinC = 1/μ₁ = 1/(3/2√2) = 2√2/3

SinC = 0.94

it is given that, sin70° = 0.94

so, C = 70°

Therefore critical angle inside the water will be 70°.