Question

As shown in the figure, an electromagnetic wave with intensity $I_I$ is incident at the interface of two media having refractive indices $n_1 = 1$ and $n_2 = \sqrt{3}$. The wave is reflected with intensity $I_R$ and transmitted with intensity $I_T$. Permeability of each medium is the same. (Reflection coefficient $R = \frac{I_R}{I_I}$ and Transmission coefficient $T = \frac{I_T}{I_I}$). Choose the correct statement(s).

• A. $R = 0$ if $\theta_I = 0^\circ$ and polarization of incident light is parallel to the plane of incidence.
• B. $T = 1$ if $\theta_I = 60^\circ$ and polarization of incident light is parallel to the plane of incidence.
• C. $R = 0$ if $\theta_I = 60^\circ$ and polarization of incident light is perpendicular to the plane of incidence.
• D. $T = 1$ if $\theta_I = 60^\circ$ and polarization of incident light is perpendicular to the plane of incidence.

Hint:

At the correct angle of incidence (\(\theta_I = 60^\circ\)) and with the appropriate polarization, total transmission can occur with \(T = 1\).

Answer 1

The Correct Option is B

In this question, we are dealing with the phenomenon of reflection and transmission of light at the interface of two media with different refractive indices. The refractive index of the first medium is \(n_1 = 1\) and the second medium is \(n_2 = \sqrt{3}\). The relationship between the reflection and transmission coefficients depends on the angle of incidence and the polarization of the incident light. Step 1: Polarization Parallel to the Plane of Incidence
When the polarization of the incident light is parallel to the plane of incidence, the reflection coefficient \(R\) depends on the angle of incidence, and it is zero at normal incidence (\(\theta_I = 0^\circ\)). Therefore, Option (A) is correct. Step 2: Polarization Perpendicular to the Plane of Incidence
For polarization perpendicular to the plane of incidence, total transmission occurs at specific angles. For $\theta_I = 60^\circ$, the transmission coefficient \(T\) is one because the light undergoes no reflection at this angle, i.e., the total transmission occurs when the polarization is perpendicular to the plane of incidence. Hence, Option (D) is correct. Thus, the correct match is Option (B). Final Answer: (B)