Name: Primary Colours of Light
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: Did you know that certain colours are more important than the others? Also, certain colours can be derived using the others! This video explains why.

Question

If the angle of incidence and angle of emergence of a light ray falling on a glass slab are

i

and

e

respectively, prove that,

i = e

.

Accepted Answer

Take a rectangular glass slab PQRS as shown in below figure:

Here, the ray AO is incident on the surface of the glass slab and undergoes refraction at the air-glass interface. The angle of incidence at this interface be $i_{1}$ and the angle of refraction be $r_{1}$ . Thus, from Snell's law of refraction, we get, $\frac{n_{g}}{n_{a}} = \frac{\sin i_{1}}{\sin r_{1}} \Rightarrow n_{g} \sin r_{1} = n_{a} \sin i_{1}$ .....(a)

Now the refracted ray OB is incident on the other surface of the glass slab and undergoes refraction at the glass-air interface. The angle of incidence at this interface be $i_{2}$ and the angle of refraction be $r_{2}$ . Thus, from Snell's law of refraction, we get, $\frac{n_{a}}{n_{g}} = \frac{\sin i_{2}}{\sin r_{2}} \Rightarrow n_{a} \sin r_{2} = n_{g} \sin i_{2}$ ....(b)

But, the angle of refraction at the first interface and the angle of incidence at the second interface are vertically opposite angles so they are equal.

Hence, $r_{1} = i_{2}$ .....(c)

Thus, from (a), (b) and (c) we get,

$n_{g} \sin r_{1} = n_{a} \sin i_{1} = n_{a} \sin r_{2} = n_{g} \sin i_{2} (∵ n_{g} \sin r_{1} = n_{g} \sin i_{2} a s r_{1} = i_{2})$

$∴ n_{a} \sin i_{1} = n_{a} \sin r_{2}$

$∴ i_{1} = r_{2}$

But $i_{1} = angle of incidence (i)$ and $r_{2} = angle of emergence (e)$ .

Therefore, $i = e$ .

If the angle of incidence and angle of emergence of a light ray falling on a glass slab are $i$ and $e$ respectively, prove that, $i = e$ .

Important Questions on Refraction of Light

Learn and Prepare for any exam you want !

If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i=e.

Important Questions on Refraction of Light

Learn and Prepare for any exam you want !

If the angle of incidence and angle of emergence of a light ray falling on a glass slab are $i$ and $e$ respectively, prove that, $i = e$ .