A : When an unpolarised light is incident on a glass plate at Brewster angle, the reflected ray and refracted ray are matually perpendicular.
R : The refractive index of glass is equal to sine of the angle of polarisation.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To solve the problem, we need to analyze the statements A and R regarding the behavior of unpolarized light at the Brewster angle.

### Step 1: Understanding the Brewster Angle
The Brewster angle (θ_B) 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.

### Step 2: Analyzing Statement A
Statement A claims that when unpolarized light is incident on a glass plate at the Brewster angle, the reflected ray and refracted ray are mutually perpendicular.
- This statement is **true**. According to the definition of Brewster's law, at the Brewster angle, the angle of reflection (θ_r) and the angle of refraction (θ_t) satisfy the relationship:
\[ θ_r + θ_t = 90^\circ \]
Hence, they are mutually perpendicular.

### Step 3: Analyzing Statement R
Statement R claims that the refractive index of glass is equal to the sine of the angle of polarization.
- This statement is **false**. According to Brewster's law, the refractive index (n) is related to the Brewster angle (θ_B) by the formula:
\[ n = \tan(θ_B) \]
Therefore, the refractive index is not equal to the sine of the angle of polarization.

### Conclusion
- Statement A is true.
- Statement R is false.

Thus, the correct answer is that A is true and R is false.

### Final Answer
A is true and R is false.

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