The polarizing angle of glass is `57^(@)` . A ray of light which is incident at this light which is incident at this angle will have an angle of refraction as

Options

A. `43^(@)`
B. `25^(@)`
C. `38^(@)`
D. `33^(@)`

Explanation

To find the angle of refraction when light is incident at the polarizing angle of glass, we can use Brewster's Law. Here's a step-by-step solution:

### Step 1: Understand Brewster's Law
Brewster's Law states that when unpolarized light hits a surface at the polarizing angle (θ_P), the reflected light is completely polarized perpendicular to the plane of incidence. The relationship between the polarizing angle and the angle of refraction is given by the equation:
\[ \theta_P + r = 90^\circ \]
where:
- \( \theta_P \) = polarizing angle
- \( r \) = angle of refraction

### Step 2: Substitute the Given Values
From the problem, we know that the polarizing angle \( \theta_P \) is \( 57^\circ \). We can substitute this value into the equation:
\[ 57^\circ + r = 90^\circ \]

### Step 3: Solve for the Angle of Refraction
To find the angle of refraction \( r \), we rearrange the equation:
\[ r = 90^\circ - 57^\circ \]
Calculating this gives:
\[ r = 33^\circ \]

### Step 4: Conclusion
Thus, the angle of refraction when light is incident at the polarizing angle of glass is:
\[ r = 33^\circ \]

### Final Answer
The angle of refraction is \( 33^\circ \).

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