Assertion:Minimum deviation by an equilateral prism of refractive index sqrt2 is `30^@.`
Reason: It is from the relation, `mu=sin((A+delta_m)/2)/sin(A/2)`

Options

A. If both Assertion and Reason are true and the Reason is 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 both Assertion is true, but the Reason is false.
D. If both Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and the reason provided, and verify if the assertion is true based on the reasoning given.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the minimum deviation (Δm) for an equilateral prism with a refractive index (μ) of √2 is 30 degrees.

2. **Understanding the Reason**:
The reason provided uses the formula for refractive index in terms of the angle of the prism (A) and the minimum deviation (Δm):
\[ \mu = \frac{\sin\left(\frac{A + \Delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]
Here, A is the angle of the prism, and Δm is the minimum deviation.

3. **Identifying Values**:
For an equilateral prism, the angle A is 60 degrees. The refractive index μ is given as √2.

4. **Substituting Values into the Formula**:
Substitute A = 60 degrees and μ = √2 into the formula:
\[ \sqrt{2} = \frac{\sin\left(\frac{60 + \Delta_m}{2}\right)}{\sin\left(\frac{60}{2}\right)} \]
Simplifying further:
\[ \sqrt{2} = \frac{\sin\left(\frac{60 + \Delta_m}{2}\right)}{\sin(30)} \]
Since \(\sin(30) = \frac{1}{2}\), we can rewrite the equation as:
\[ \sqrt{2} = 2 \sin\left(\frac{60 + \Delta_m}{2}\right) \]
This simplifies to:
\[ \frac{1}{\sqrt{2}} = \sin\left(\frac{60 + \Delta_m}{2}\right) \]

5. **Finding the Angle**:
The value of \(\frac{1}{\sqrt{2}}\) corresponds to an angle of 45 degrees. Therefore:
\[ \frac{60 + \Delta_m}{2} = 45 \]

6. **Solving for Δm**:
Multiply both sides by 2:
\[ 60 + \Delta_m = 90 \]
Subtract 60 from both sides:
\[ \Delta_m = 30 \text{ degrees} \]

7. **Conclusion**:
The assertion is true, as we have shown that the minimum deviation for an equilateral prism with a refractive index of √2 is indeed 30 degrees. The reason provided is also valid as it correctly explains how to derive the assertion.

### Final Answer:
Both the assertion and the reason are true.

---