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, we need to find the Brewster's angle (θ_B) at which unpolarised light is completely plane polarised when incident on a glass plate with a refractive index (μ) of 1.54.

### Step-by-Step Solution:

1. **Understanding Brewster's Angle:**
Brewster's angle is defined as the angle of incidence at which light with a particular polarisation is perfectly transmitted through a transparent dielectric surface, with no reflection. At this angle, the reflected and refracted rays are perpendicular to each other.

2. **Using the Relation for Brewster's Angle:**
The relationship for Brewster's angle is given by:
\[ \tan(\theta_B) = \mu \]
where \( \mu \) is the refractive index of the medium.

3. **Substituting the Given Refractive Index:**
From the problem, we know that the refractive index of the glass plate is:
\[ \mu = 1.54 \]
Therefore, we can write:
\[ \tan(\theta_B) = 1.54 \]

4. **Finding the Angle:**
We are given that \( \tan(57^\circ) = 1.54 \). Thus, we can equate:
\[ \theta_B = 57^\circ \]

5. **Conclusion:**
The angle of polarisation (Brewster's angle) at which the unpolarised light is completely plane polarised is:
\[ \theta_B = 57^\circ \]

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

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