Question

Explain what is critical angle?

Answer 1

Refraction:

1. When a light wave passes from one medium to another, it bends and gets redirected due to the difference in its speed in the two mediums. This process of redirection of waves is known as refraction.
2. An imaginary line perpendicular to the surface at the point of incidence of the wave is called normal. When light passes from a rarer to a denser medium, it bends toward the normal, and when light passes from a denser to a rarer medium, it bends away from the normal.
3. The angle that the incident ray makes with the normal is called the angle of incidence $\left(i\right)$ and the angle that the refracted ray makes with the normal is called the angle of refraction $\left(r\right)$.

Critical angle:

1. A critical angle is a maximum angle at which a ray of light traveling from one medium to another can be incident without being totally reflected.
2. The critical angle $\left(i_c\right)$ is the angle of incidence in an optically denser medium for which the angle of refraction is $90°$.
3. When the angle of incidence is greater than the critical angle, the process of total internal reflection occurs. That is, the way gets completely reflected.

Formula of critical angle:

1. According to Snell's law, ${\mu }_1\sin i={\mu }_2\sin r$, where ${\mu }_1$ and ${\mu }_2$ are refractive indices of the medium from which it comes and the medium to which it passes, respectively.
2. So, for the critical angle, the above expression can be written as ${\mu }_1\sin i_c={\mu }_2\sin 90°$.
3. Solve it further to obtain the formula for critical angle

$$\begin{gathered} {\mu }_1\sin i_c={\mu }_2\sin 90° \\ \Rightarrow {\mu }_1\sin i_c={\mu }_2\left[\because \sin 90°=1\right] \\ \Rightarrow \sin i_c=\frac{{\mu }_2}{{\mu }_1} \\ \Rightarrow {\mathit{i}}_{\mathbf{c}}\mathbf{=}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{{\mathbf{\mu }}_{\mathbf{2}}}{{\mathbf{\mu }}_{\mathbf{1}}}\mathbf{\right)} \end{gathered}$$

Hence, the critical angle $\left({\mathit{i}}_{\mathit{c}}\right)$ is the angle of incidence in an optically denser medium for which the angle of refraction is $\mathbf{90}\mathbf{°}$. The mathematical expression for critical angle is ${\mathit{i}}_{\mathbf{c}}\mathbf{=}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{-}\mathbf{1}}\mathbf{\left(}\frac{{\mathbf{\mu }}_{\mathbf{2}}}{{\mathbf{\mu }}_{\mathbf{1}}}\mathbf{\right)}$.