An unpolarised light is incident upon a glass plate of refractive index 1.54 at Brewster's angle and gets completely plane polarised. The angle of polarisation is (given tan `57^(@)` = 1.54)

Options

A. `57^(@)`
B. `46^(@)`
C. `33^(@)`
D. `82^(@)`

Answer

To solve the problem of finding the angle of polarization when unpolarized light is incident upon a glass plate at Brewster's angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Brewster's Angle**: Brewster's angle (θp) is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. At this angle, the reflected light is completely polarized.

2. **Use the Brewster's Angle Formula**: The relationship between Brewster's angle and the refractive index (μ) of the medium is given by:
\[ \tan(\theta_p) = \mu \]
where θp is Brewster's angle and μ is the refractive index of the medium (in this case, glass).

3. **Given Data**: We know that the refractive index of the glass plate is μ = 1.54.

4. **Substituting the Value**: According to the formula:
\[ \tan(\theta_p) = 1.54 \]

5. **Finding θp**: To find θp, we take the arctangent (inverse tangent) of 1.54:
\[ \theta_p = \tan^{-1}(1.54) \]

6. **Calculating θp**: Using a calculator or trigonometric tables, we find:
\[ \theta_p \approx 57^\circ \]

7. **Conclusion**: The angle of polarization when unpolarized light is incident upon the glass plate at Brewster's angle is:
\[ \theta_p = 57^\circ \]

### Final Answer:
The angle of polarization is \( 57^\circ \).

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