A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be : (Given: relative permeability of medium `mu_r = 1`)

Options

A. `10^(@)`
B. `20^(@)`
C. `30^(@)`
D. `60^(@)`

Explanation

To solve the problem, we need to determine the angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium. This occurs when the angle of incidence exceeds the critical angle for total internal reflection.

### Step-by-Step Solution:

1. **Identify the Dielectric Constant**:
The dielectric constant (ε) of the medium is given as 4.

2. **Calculate the Refractive Index**:
The refractive index (n) of a medium can be calculated using the formula:
\[ n = \sqrt{\epsilon_r} \]
where ε_r is the relative permittivity (dielectric constant). Here, since the relative permeability (μ_r) is given as 1, we can ignore it for the calculation of the refractive index.

\[ n = \sqrt{4} = 2 \]

3. **Identify the Refractive Index of Air**:
The refractive index of air (n_air) is approximately 1.

4. **Determine the Critical Angle**:
The critical angle (θ_c) can be determined using Snell's law:
\[ n_1 \sin(\theta_c) = n_2 \sin(90^\circ) \]
where \( n_1 \) is the refractive index of the denser medium (2), and \( n_2 \) is the refractive index of air (1). Thus, we have:
\[ 2 \sin(\theta_c) = 1 \cdot 1 \]
Rearranging gives:
\[ \sin(\theta_c) = \frac{1}{2} \]

5. **Calculate the Critical Angle**:
The critical angle can be calculated as:
\[ \theta_c = \sin^{-1}\left(\frac{1}{2}\right) = 30^\circ \]

6. **Condition for Total Internal Reflection**:
For total internal reflection to occur, the angle of incidence (i) must be greater than the critical angle:
\[ i > \theta_c \]
Therefore, we have:
\[ i > 30^\circ \]

7. **Conclusion**:
The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium must be greater than 30 degrees.

### Final Answer:
The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium is greater than 30 degrees.

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