Question
Write Snell's law and derive its general equation.
✓
Answer
→Snell's Law : For a given two medium the ratio of the sine of the angle of incidence to the sine of angle of refraction is constant.
$\frac{\sin i}{\sin r}=n_{21}......(1)$
where, $n_{21}$ is the refractive index of the second medium with respect to the first medium.
→absolute refractive index of medium (1),
$n_1=\frac{C}{v_1}$
absolute refractive index of medium (2),
$n_2=\frac{ C }{ v _2}$
(where, C is the velocity of light in vacuum.)
$\begin{array}{l}\therefore n_{21}=\frac{v_1}{v_2} \text { and } \frac{n_2}{n_1}=\frac{v_1}{v_2} \\\therefore n_{21}=\frac{n_2}{n_1}......(2)\end{array}$
→From equation (1) and equation (2),
$\begin{array}{l}\therefore \frac{\sin i}{\sin r}=\frac{n_2}{n_1} \\\therefore n_1 \sin i=n_2 \sin r\end{array}$
→This is called the general equation of Snell's law.
$\frac{\sin i}{\sin r}=n_{21}......(1)$
where, $n_{21}$ is the refractive index of the second medium with respect to the first medium.
→absolute refractive index of medium (1),
$n_1=\frac{C}{v_1}$
absolute refractive index of medium (2),
$n_2=\frac{ C }{ v _2}$
(where, C is the velocity of light in vacuum.)
$\begin{array}{l}\therefore n_{21}=\frac{v_1}{v_2} \text { and } \frac{n_2}{n_1}=\frac{v_1}{v_2} \\\therefore n_{21}=\frac{n_2}{n_1}......(2)\end{array}$
→From equation (1) and equation (2),
$\begin{array}{l}\therefore \frac{\sin i}{\sin r}=\frac{n_2}{n_1} \\\therefore n_1 \sin i=n_2 \sin r\end{array}$
→This is called the general equation of Snell's law.
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