Question

The critical angle of a crystal is 30°. Its Brewster angle is _____________ degrees. (Round off to the nearest integer).

Answer 1

Correct Answer: 27

1. Find the Refractive Index ($\mu$)

The relationship between the critical angle ($\theta_c$) and the refractive index ($\mu$) is given by:

 

$$\mu = \frac{1}{\sin \theta_c}$$

Given $\theta_c = 30^\circ$:

 

$$\mu = \frac{1}{\sin 30^\circ} = \frac{1}{0.5} = 2$$

2. Find the Brewster Angle ($\theta_B$)

According to Brewster's Law, the tangent of the Brewster angle (polarizing angle) equals the refractive index of the material:

 

$$\tan \theta_B = \mu$$

Substitute $\mu = 2$:

 

$$\tan \theta_B = 2$$

$$\theta_B = \tan^{-1}(2)$$

3. Calculate the Value

Using the inverse tangent function:

 

$$\theta_B \approx 63.43^\circ$$

4. Round Off

The problem asks to round off to the nearest integer.

 

$$63.43^\circ \approx 63^\circ$$

Final Answer:

The Brewster angle is 63 degrees.