Name: Brewster’s Law
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: Light is a transverse electromagnetic wave with electric field vectors vibrating in infinite directions perpendicular to the direction of propagation. Let's...

Question

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.

Accepted Answer

The ratio of the velocity of light in vacuum to the velocity of light in the specified medium is called refractive index.

$μ = \frac{c}{v}$

where $c$ is the speed of light in vacuum and $v$ is the velocity of the light in the given medium.

It is also defined as the sine of the angle of incidence to the angle of refraction.

$μ = \frac{\sin i}{\sin r}$

Let us assume a plane wave $‐$ front $AB$ propagating in a denser medium is incident on the interface $PP'$ at angle $i$ . Let $t$ be the time taken by the wave $‐$ front to travel the distance $BC$ . If $v_{1}$ is the speed of light in medium $I$ , then

$BC = v_{1} t$

In order to find the shape of the refracted wave $‐$ front, let us draw a sphere of radius $AE$ . Let $v_{2}$ be the speed of light in medium $II$ , then, $AE = v_{2} t$ . The tangent plane $CE$ represents the refracted wave $‐$ front.
Hence, in $∆ ABC :$ $\sin i = \frac{BC}{AC} = \frac{v_{1} t}{AC}$
In $∆ ACE : \sin r = \frac{AE}{AC} = \frac{v_{2} t}{AC}$
Therefore, $\frac{\sin i}{\sin r} = \frac{BC}{AE} = \frac{v_{1}}{v_{2}}$

Since, $μ_{1} = \frac{c}{v_{1}} and μ_{2} = \frac{c}{v_{2}}$

Therefore, $\frac{\sin i}{\sin r} = \frac{v_{1}}{v_{2}} = \frac{μ_{2}}{μ_{1}}$

$\Rightarrow μ_{1} \sin i = μ_{2} \sin r$

This is known as the Snell $'$ s law of refraction.

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.

Important Questions on Wave Optics

Learn and Prepare for any exam you want !

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.

Important Questions on Wave Optics

Learn and Prepare for any exam you want !

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.