Calculate the angle of emergence (e) of the ray of light incident normally on the face AC of a glass prism ABC of refractive index `sqrt(3)`. How will the angle of emergence change qualitatively, if the ray of light emerges from the prism into a liquid of refractive index 1.3 instead of air ?

Explanation

As shown in the diagram, the angle of incidence Zi at the face AB of glass prism ABC is `30^(@)` and refractive index of glass prism n =` sqrt(3)` .
If `anglee` be the angle of emergence in air medium then as per snell.s law:
`(sin i)/(sin e) = n_(ag) = (1)/(n_(gn))implies ( sin 30^(@))/(sin e) = (1)/(sqrt(3))`
`implies sin e = sqrt(3) xx sin 30^(@) = (sqrt(3))/(2) implies e= sin^(-1) ((sqrt(3))/(2))= 60^(@)`

If the prism is immersed in a liquid of refractive index `n_(g), = 1.3`, then new angle of emergence e will be given by :
`(sin i)/(sin e) = (1)/(n_(g)) or sin e= n_(gl)xx sin I = (sqrt(3))/(1.3) xx sin 30^(@)`
`implies sin e = (sqrt(3))/(1.3) xx(1)/(2) = (1)/(1.3) ((sqrt(3))/(2))`
Obviously sin e. `lt` sin e and hence e. `lt` e. So the angle of emergence decreases when the prism is immersed in the liquid.