Question

(a) A ray of light is incident normally on the face AB of a right-angled glass prism of refractive index _aμ_g 1.5. The prism is partly immersed in a liquid of an unknown refractive index. Find the value of the refractive index of the liquid so that the ray grazes along the face BC after refraction through the prism.

(b) Trace the path of the rays if it were incident normally on the face AC.

Answer 1

(a) 

Given the refractive index of prism μg= 1.5 the ray will grazes along the face BC when the angle of incidence i is equal to the critical angle for the glass and liquid interface here i = 60° (from the fig.)and sin i = `mu_"l"/mu_"g"`

`mu_"l" = mu_"g" sin "i"`

`mu_"l" = 1.5 sin 60°`

`mu_"l" = 1.3`

So the refractive index of the liquid is 1.3

(b)

The angle of incidence for ray 1 and ray 2 on face BC is equal to 30°For ray 1

The critical angle for glass-air interface is

`sin "i"_"c" = mu_"a"/mu_"g" = (1.3)/(1.5) = 0.866`

`"i"_"c" = 60°`

Now since the angle of incidence is smaller than the critical angle refraction will take place as shown in figure