Question 84: Ray Optics

Question

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is $\_\_\_\_$

Accepted Answer

Light hits the surface at an angle of incidence $i$.
Part of the light bounces back. According to the Law of Reflection, the angle of reflection is equal to the angle of incidence (i).
Part of the light enters the second medium. It bends at an angle of refraction $r$.
The reflected and refracted rays are perpendicular to each other. This means the angle between the reflected ray and the refracted ray is $90^{\circ}$.
The sum of angles on a straight line is $180^{\circ}$.
$$ \mathrm{i}+90^{\circ}+\mathrm{r}=180^{\circ} \Rightarrow \mathrm{i}+\mathrm{r}=90^{\circ} $$
$$ \Rightarrow \mathrm{r}=90^{\circ}-\mathrm{i} $$
Now using the fundamental law of refraction, Snell's Law :
$$ \mu_1 \sin (\mathrm{i})=\mathrm{n}_2 \sin (\mathrm{r}) \Rightarrow \mu_1 \sin (\mathrm{i})=\mathrm{n}_2 \sin \left(90^{\circ}-\mathrm{i}ight) $$
$\Rightarrow \mu_1 \sin (\mathrm{i})=\mathrm{n}_2 \cos (\mathrm{i})$
$$\Rightarrow $$ $$ 	an (\mathrm{i})=\frac{\mu_2}{\mu_1} $$
The refractive index of first medium is $\mu_1=2$ and the refractive index of second medium is $\mu_2=2 \sqrt{3}$
$$ 	an (i)=\frac{2 \sqrt{3}}{2}=\sqrt{3} \Rightarrow i=60^{\circ} $$
Therefore, the angle of incidence is $60^{\circ}$.
Hence, the correct option is (B).

Answer

$45^{\circ}$

Answer

$60^{\circ}$

Answer

$10^{\circ}$

Answer

$30^{\circ}$

Ray Optics

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and 2 \sqrt{3} (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is \_\_\_\_

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