Question

Consider two adjacent transparent media. The speed of light in Medium $1$ is $v_1$, and the speed of light in Medium $2$ is $v_2$. If $v_1<v_2$, Find out the condition on incident beam for total internal reflection at the interface between these media :

• A. Incident in Medium $1$ and strikes the interface at an angle of incidence greater than ${\sin }^{-1}\left(v_1/v_2\right)$
• B. Incident in Medium $1$ and strikes the interface at an angle of incidence greater than ${\sin }^{-1}\left(v_2/v_1\right)$
• C. Incident in Medium $2$ and strikes the interface at an angle of incidence greater than ${\sin }^{-1}\left(v_1/v_2\right)$
• D. Incident in Medium $2$ and strikes the interface at an angle of incidence greater than ${\sin }^{-1}\left(v_2/v_1\right)$
• E. Total internal reflection is impossible in the situation described

Answer 1

The correct option is A Incident in Medium $1$ and strikes the interface at an angle of incidence greater than ${\sin }^{-1}\left(v_1/v_2\right)$

For the total internal reflection, the beam must be incident in the higher refractive index medium and strike the interface at an angle of incidence greater than the critical angle.

The refractive index of medium 1 is $n_1=c/v_1$ and the refractive index of medium 2 is $n_2=c/v_2$.

As $v_1<v_2$, the refractive index of medium 1 will be higher.

Using Snell's law for total internal reflection, ${\sin }_{{\theta }_c}=n_2/n_1$

or ${\theta }_c={\sin }^{-1}\left(v_1/v_2\right)$