Answer:
a) θ₁ = 48.6º angle of incidence must be greater than this value for the ray to be reflected
b) θ₁ = 49.8º, the angle of incidence is greater than this value, the ray is reflected.
Step-by-step explanation:
When a ray of light passes from one medium to another it must comply with the law of refraction, in the case of the incident medium it has a refractive index greater than the medium to which it must transmit, total internal reflection can occur
n₁ sin θ₁ = n₂ sin θ₂
where we use subscript 1 for the incident medium and subscript 2 for the refracted medium.
In the case of θ₂ = 90, the sin 90 = 1, internal total reflection occurs.
sin θ₁ = n₂ / n₁
the medium where it is transmitted is air with n₂ = 1
in the first diagram the incident medium is water with n₁ = 1,333
let's calculate the angle of incidence for the total internal reflection to occur
sin θ₁ = 1 / 1,333
θ₁ = sin⁻¹ 0.7502
θ₁ = 48.6º
the angle of incidence must be greater than this value for the ray to be reflected
second case the refractive index of ice is n₁ = 1.309
sin θ₁ = 1 / 1.309
θ₁ = sin⁻¹ 0.7639
θ₁ = 49.8º
as the angle of incidence is greater than this value, the ray is reflected.