When light is incident from air to glass at an angle `57^@`, the reflected beam is completely polarised. If the same beam is incident from water to glass, the angle of incidence at which reflected beam is completely polarised will be

Options

A. (a) `theta=57^@`
B. (b) `thetagt57^@`
C. (c) `thetalt57^@`
D. (d) cannot be determined

Explanation

To solve the problem, we need to determine the angle of incidence at which the reflected beam is completely polarized when light is incident from water to glass. We will use Brewster's Law, which states that the angle of incidence at which light is completely polarized upon reflection is given by the formula:

\[ \tan(\theta_B) = \mu \]

where \(\theta_B\) is Brewster's angle and \(\mu\) is the refractive index of the second medium relative to the first medium.

### Step-by-Step Solution:

1. **Identify the given information:**
- The angle of incidence from air to glass where the reflected beam is completely polarized is \(57^\circ\).
- This angle corresponds to Brewster's angle when light travels from air (refractive index \(n_1 = 1\)) to glass (refractive index \(n_2\)).

2. **Calculate the refractive index of glass:**
- Using Brewster's Law for air to glass:
\[ \tan(57^\circ) = n_{glass} \]
- Calculate \(\tan(57^\circ)\):
\[ \tan(57^\circ) \approx 1.5399 \]
- Therefore, the refractive index of glass is approximately \(n_{glass} \approx 1.54\).

3. **Determine the refractive index of water:**
- The refractive index of water is approximately \(n_{water} \approx 1.33\).

4. **Apply Brewster's Law for water to glass:**
- When light is incident from water to glass, we need to find the new Brewster's angle \(\theta_B'\):
\[ \tan(\theta_B') = \frac{n_{glass}}{n_{water}} \]
- Substitute the values:
\[ \tan(\theta_B') = \frac{1.54}{1.33} \]
- Calculate \(\tan(\theta_B')\):
\[ \tan(\theta_B') \approx 1.157 \]

5. **Calculate the new Brewster's angle:**
- Now, find \(\theta_B'\):
\[ \theta_B' = \tan^{-1}(1.157) \]
- Calculate \(\theta_B'\):
\[ \theta_B' \approx 48.37^\circ \]

6. **Conclusion:**
- The angle of incidence at which the reflected beam is completely polarized when light is incident from water to glass is approximately \(48.37^\circ\).

### Final Answer:
The angle of incidence at which the reflected beam is completely polarized when light is incident from water to glass is approximately \(48.37^\circ\).