Question

From Snell's law, why with the increase in the angle of the incident ray of rarer medium increases the angle of refraction of denser medium.

Answer 1

Refraction angle increases less rapidly when angle of incidence increases.

From Snell’s law

μ=Sini/Sinr

=> Sinr=Sini/μ −−−−> Eq 1

Cosr=√(1−Sin2r)

=> Cosr=√(1−Sin2i/μ2)

Differentiating Eq 1,

Cosr(dr/di)=Cos(i/μ)

=> dr/di=Cos(i/μ1)/(√(1−Sin2i/μ2))

dr/di=Cosi/√(μ2−Sin2i)

dr/di=1/√(μ2Sec2i−tan2i)

dr/di=1/√(μ2+(μ2−1)tan2i)

Now, when i increases tan² (i ) increases => denominator increases => total value of the expression decreases. You can also observe that when i approaches 90˚, dr/di approaches 0.