Brewster angle for air to water transition is (refractive index of water is `4/3`)

Options

A. `sin^-1 3/4`
B. `cos^-1 3/4`
C. `tan^-1 3/5`
D. `cot^-1 3/4`

Answer

To find the Brewster angle for the transition from air to water, 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 and refracted rays are perpendicular to each other.

2. **Formula for Brewster's Angle**: The Brewster angle can be calculated using the formula:
\[ \tan(\theta_p) = n \]
where \( n \) is the refractive index of the second medium (water in this case) relative to the first medium (air).

3. **Identify the Refractive Index**: The refractive index of water is given as \( n = \frac{4}{3} \).

4. **Calculate Brewster's Angle**: Using the formula, we can substitute the value of the refractive index:
\[ \tan(\theta_p) = \frac{4}{3} \]

5. **Find θp**: To find the Brewster angle, we take the arctangent (inverse tangent) of the refractive index:
\[ \theta_p = \tan^{-1}\left(\frac{4}{3}\right) \]

6. **Calculate the Angle**: Using a calculator or trigonometric tables, we can find:
\[ \theta_p \approx 53.13^\circ \]

### Final Answer:
The Brewster angle for the air to water transition is approximately \( 53.13^\circ \).

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