9.4 Figures 9.31(a) and (b) show the 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 the glass when the angle of incidence in water is 45° with the normal to a water-glass interface [Fig. 9.31(c)].

Figure 9.31

Hint: Apply snell's law

Step 1: Find the refractive index of glass.
For the glass-air interface:
Angle of incidence, i =60°
Angle of refraction, r=35°
The relative refractive index of the glass with respect to air,

Step 2: Find the refractive index of water.
For the air-water interface:
The angle of incidence, i=
The angle of refraction, r=

Step 3: Find the refractive index of glass with respect to water.
The relative refractive index of glass with respect to water:
\(\mu_{gw}=\frac{\mu_{ga}}{\mu_{wa}}=\frac{\frac{sin60^{0}}{sin35^{0}}}{\frac{sin60^{0}}{sin47^{0}}}=\frac{sin47^{0}}{sin35^{0}}\)

Angle of incidence

Step 4: Find the angle of refraction at the water-glass interface.
For the glass-water interface:
The angle of incidence, i= 
Let the angle of refraction = r
From Snell’s law,
μgw=sinisinr
sin47°sin35°=sin45sinr
sinr=121.275=0.5546
 r=sin-10.5546=38.68
Hence, the angle of refraction at the water-glass interface is 38.68°.