# Q 9.4    Figures of (a) and (b) show refraction of a ray in air incident at $60^{\circ}$ 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 $45^{\circ}$ with the normal to a water-glass interface [Fig.(c)].

As we know,by snell's law

$\mu_1sin\theta _1=\mu _2sin\theta _2$  where,

$\mu_1$ = refrective index of medium 1

$\theta _1$ = incident angle in medium 1

$\mu _2$ = refrective index of medium 2

$\theta _2$ = refraction angle in medium 2

NOW, APPLYING IT FOR fig (a)

$1sin60=\mu _{glass}sin35$

$\mu _{glass}=\frac{sin60}{sin35}=\frac{0.866025}{0.573576 } = 1.509$

Now applying for fig (b)

$1sin60=\mu _{water}sin47$

$\mu _{water}=\frac{sin60}{sin47}=\frac{.8660}{.7313} = 1.184$

Now in fig (c) Let refraction angle be $\theta$ so,

$\mu _{water}sin45=\mu _{glass}sin\theta$

$sin\theta =\frac{\mu _{water}*sin45}{\mu _{glass}}$

$sin\theta =\frac{1.184*0.707}{1.509} = 0.5546$

$\theta = sin^{-1}(0.5546) = 38.68$

Therefore the angle of refraction when ray goes from water to glass in fig(c) is 38.68.

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