For the same value of angle of incidence, the angles of refraction in three media $A$ , $B$ and $C$ are $15^{o}$ , $25^{o}$ and $35^{o}$ respectively. In which medium would the velocity of light be minimum?

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Solution

Let the refractive index of the medium be $n$ and speed of light in air is $c$ .
Using Snell's law of refraction : $n_{a i r} \times s i n i = n_{m e d i u m} \times s i n r$ where $n_{a i r} = 1$
$∴$ $1 \times s i n i = n \times s i n r$ $⟹ n = \frac{s i n i}{s i n r}$

Velocity of light in a medium $v = \frac{c}{n} = \frac{c \times s i n r}{s i n i}$ $⟹ v \propto s i n$ $r$
Thus velocity of light is minimum in medium A.

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For the same value of angle of incidence, the angles of refraction in three media A, B and C are 15o, 25o and 35o respectively. In which medium would the velocity of light be minimum?

Let the refractive index of the medium be n and speed of light in air is c.Using Snell's law of refraction : nair×sini=nmedium×sinr where nair=1∴ 1×sini=n×sinr ⟹n=sinisinrVelocity of light in a medium v=cn=c×sinrsini ⟹v∝sin rThus velocity of light is minimum in medium A.

For the same value of angle of incidence, the angles of refraction in three media $A$ , $B$ and $C$ are $15^{o}$ , $25^{o}$ and $35^{o}$ respectively. In which medium would the velocity of light be minimum?