If relative permittivity and relative permeability of a medium are 3 and `4/3` respectively. the critical angle for this medium is.

Options

A. `45^@`
B. `60^@`
C. `30^@`
D. `15^@`

Explanation

To find the critical angle for a medium with given relative permittivity and relative permeability, we can follow these steps:

### Step 1: Understand the concept of critical angle
The critical angle is the angle of incidence above which total internal reflection occurs. It can be calculated using Snell's law, where the angle of refraction is 90 degrees.

### Step 2: Write down Snell's law for critical angle
According to Snell's law:
\[ n_1 \sin(\theta_c) = n_2 \sin(90^\circ) \]
Here, \(n_1\) is the refractive index of the medium and \(n_2\) is the refractive index of the second medium (usually air, with \(n_2 = 1\)).

### Step 3: Rearrange the equation for critical angle
Since \(\sin(90^\circ) = 1\), we can simplify the equation to:
\[ \sin(\theta_c) = \frac{n_2}{n_1} = \frac{1}{n_1} \]

### Step 4: Calculate the refractive index of the medium
The refractive index \(n\) of a medium can be calculated using the formula:
\[ n = \sqrt{\mu_r \epsilon_r} \]
where \(\mu_r\) is the relative permeability and \(\epsilon_r\) is the relative permittivity.

Given:
- \(\epsilon_r = 3\)
- \(\mu_r = \frac{4}{3}\)

Substituting these values:
\[ n = \sqrt{3 \times \frac{4}{3}} = \sqrt{4} = 2 \]

### Step 5: Substitute the refractive index into the critical angle equation
Now, substituting \(n_1 = 2\) into the equation for critical angle:
\[ \sin(\theta_c) = \frac{1}{2} \]

### Step 6: Calculate the critical angle
To find \(\theta_c\):
\[ \theta_c = \arcsin\left(\frac{1}{2}\right) = 30^\circ \]

### Final Answer
The critical angle for the medium is \(30^\circ\).

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