Assertion : The refractive index of diamond is `sqrt(6)` and that of liquid is `sqrt(3)` . If the light travels from diamond to the liquid, it will totally reflected when the angle of incidence is `30^(@)`.
Reason : `mu=1/(sin C)`, where `mu` is the refractive index of diamond with respect to liquid.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion
B. If both assertion and reason are true but reason is not the correct explanation of the assertion
C. If assertion is true but reason is false
D. If assertion is f alse but reason is true

Answer

To solve the problem, we need to analyze both the assertion and the reason provided in the question regarding the behavior of light as it travels from diamond to a liquid.

### Step 1: Understand the refractive indices
The refractive index of diamond (\( \mu_d \)) is given as \( \sqrt{6} \) and that of the liquid (\( \mu_l \)) is \( \sqrt{3} \).

### Step 2: Calculate the refractive index of diamond with respect to the liquid
The refractive index of diamond with respect to the liquid is given by:
\[ \mu = \frac{\mu_d}{\mu_l} = \frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2} \]

### Step 3: Determine the critical angle for total internal reflection
The critical angle (\( C \)) can be calculated using Snell's law, which states:
\[ \mu_d \sin C = \mu_l \sin 90^\circ \]
This simplifies to:
\[ \sin C = \frac{\mu_l}{\mu_d} = \frac{\sqrt{3}}{\sqrt{6}} = \frac{1}{\sqrt{2}} \implies C = 45^\circ \]

### Step 4: Analyze the angle of incidence
The angle of incidence given in the assertion is \( 30^\circ \). For total internal reflection to occur, the angle of incidence must be greater than the critical angle. Since \( 30^\circ < 45^\circ \), total internal reflection will not occur.

### Step 5: Conclusion on the assertion
Since the angle of incidence (30°) is less than the critical angle (45°), the assertion that light will be totally reflected is **false**.

### Step 6: Evaluate the reason statement
The reason states that \( \mu = \frac{1}{\sin C} \). This is a correct relationship for the refractive index in terms of the critical angle. Since we calculated the critical angle correctly, the reason is **true**.

### Final Conclusion
- **Assertion**: False
- **Reason**: True