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 Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Understanding the Assertion
The assertion states that the refractive index of diamond is \( \sqrt{6} \) and that of the liquid is \( \sqrt{3} \). We need to determine if total internal reflection (TIR) occurs when light travels from diamond to the liquid at an angle of incidence of \( 30^\circ \).

### Step 2: Calculate the Critical Angle
To find the critical angle \( \theta_c \) for total internal reflection, we use the formula:
\[ \sin \theta_c = \frac{n_2}{n_1} \]
where \( n_1 \) is the refractive index of diamond and \( n_2 \) is the refractive index of the liquid.

Substituting the values:
\[ n_1 = \sqrt{6}, \quad n_2 = \sqrt{3} \]
\[ \sin \theta_c = \frac{\sqrt{3}}{\sqrt{6}} = \frac{\sqrt{3}}{\sqrt{2 \cdot 3}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \]
Thus, the critical angle \( \theta_c \) can be calculated as:
\[ \theta_c = \sin^{-1}\left(\frac{\sqrt{2}}{2}\right) = 45^\circ \]

### Step 3: Compare the Angle of Incidence with the Critical Angle
The angle of incidence given is \( 30^\circ \). Since \( 30^\circ < 45^\circ \), the angle of incidence is less than the critical angle.

### Step 4: Conclusion on the Assertion
Since the angle of incidence is less than the critical angle, total internal reflection will not occur. Therefore, the assertion is **false**.

### Step 5: Analyzing the Reason
The reason states that \( \mu = \frac{1}{\sin C} \), where \( \mu \) is the refractive index of diamond with respect to the liquid. This is a correct statement, as it relates the refractive indices and the critical angle.

### Final Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, and the reason is true.

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