Figures 9.31(a) and (b) show refraction of a ray in air incident at 60° with the normal to a glass-air and water-air interface, respectively. Predict the angle of refraction in glass when the angle of incidence in water is 45° with the normal to a water-glass interface [Fig. 9.31(c)].

Explanation

For (a), refractive index of glass with respect to air,
`""^(a)mu_g = (sin i)/(sin r) = (sin 60^@)/(sin 35^@) = (0.8660)/(0.5736) = 1.51 `
(b) Refactive index of glass with respect to air,
`""^(a) mu_(W) = (sin i)/(sin r) = (sin 60^@)/(sin 47^@) = (0.8660)/(0.6561) = 1.32 `
(c) Refractive index of glass w.r.t water.
`""^(w)mu_(g) = (a_(mug))/(a_(mug))= 1.51/1.32= 1.144`
`""^(w)mug = (sin i)/(sinr) = (sin 45^@)/(sinr)`
`(""^(a)mu_g)/(""^(a)mu_g) = (sin 45^@)/(sinr )`
`therefore (1.51)/(1.32) = (0.7071)/(sinr)`
`therefore sin r = (0.7071)/(sinr)`
`therefore sin r = (0.7071 xx 1.32)/(1.51) = 0.6181`
From log table ` r = 38.2^@`