Question

The refractive index of a prism is 2. The prism can have a maximum refracting angle of
A.$90{}^\circ$
B.$60{}^\circ$
C.$45{}^\circ$
D.$30{}^\circ$

Answer 1

For this question we will use the concept of critical angle. Refractive index of prism is given in the question. By calculating the critical angle of the prism we can determine the angle made inside the prism.

Formula used:
${{\theta }_{c}}={{\sin }^{-1}}\left( \dfrac{1}{r} \right)$

Complete step by step answer:
Refractive is a measure of how much a material is denser. In other ways it is the change in speed of light in different mediums.
The refractive index of prism is given. We have to calculate the maximum refractive angle.
Let us consider be the critical angle and be the refractive index then
${{\theta }_{c}}={{\sin }^{-1}}\left( \dfrac{1}{r} \right)$
$={{\sin }^{-1}}\left( \dfrac{1}{2} \right)=30{}^\circ$
The light rays travel from air to prism. So the angle that the light ray forms inside the prism will be greater than the critical angle i.e. $30{}^\circ$.
$A={{r}_{1}}+{{r}_{2}}$
If we consider that A is greater than $60{}^\circ$ then the ray does not come out of the prism. Therefore, maximum refracting angle can be $60{}^\circ$ . Thus option B is correct.

Additional information:
Refractive index is a dimensionless quantity which describes the speed of light i.e. how slow or fast light travels in a medium. Refractive index can be applied for identifying any substance, its purity or its concentration. It works on the principle of refraction.

Note:
Critical angle can be defined as the angle of incidence for which the angle of refraction is $90{}^\circ$ . The condition for formation of critical angle is that the ray should travel from denser medium to rarer medium/ less denser medium. The wavelength of refracted rays should be more for the formation of critical angles.