Help me to complete the given ray diagram ​

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.

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.

we can see how the government has failed them.