Define the term, “refractive index” of a medium. Verify Snell’s law of refraction when a plane wavefront is propagating from a denser to a rarer medium.

The ratio of the speed of light in vaccum to the speed of light in the medium is termed as '' refractive index '' of  medium.

Let us consider the medium I, which is optically denser than medium 2.

Let the speed of light be $v_{1}$ in medium I and $v_{2}$ in medium II.

Always, note that $v_{2} > v_{1}$

A plane wave AB propagates and hits the interface at an angle i. and  can be the time taken be the wavefront to travel the distance BC.

Now, we want to draw the refracted wavefront.

We can draw a sphere of radius $v_{2}$  with A as centre. Let the surface tangent to the sphere passing through point C, as the refracted wavefront.

Now,

Let the surface be tangent to the sphere at E.

In $\Delta ABC$

$\sin \; i = \frac{v_{1}t}{AC}$ and,

In $\Delta AEC$ $\iota$

$\sin \; r = \frac{v_{2}t}{AC}$

On dividing both the equations, we finally have,

$\frac{\sin i}{\sin r}=\frac{v_{1}}{v_{2}}=\frac{c/v_{2}}{c/v_{1}}$

Hence, $\frac{\sin i}{\sin r}=\frac{n_{2}}{n_{1}}$

This is the verified snell's law.

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