Assertion : The focal length of an equiconvex lens placed in air is equal to radius of curvature of either face.
Reason : For an equiconvex lens radius of curvature of both the faces is same.

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

Explanation

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

### Step 1: Understand the Assertion
The assertion states that the focal length (f) of an equiconvex lens placed in air is equal to the radius of curvature (R) of either face of the lens.

### Step 2: Understand the Reason
The reason states that for an equiconvex lens, the radius of curvature of both faces is the same. This is indeed true, as an equiconvex lens has two convex surfaces with equal radii of curvature.

### Step 3: Use the Lensmaker's Formula
The lensmaker's formula is given by:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where:
- \( \mu \) is the refractive index of the lens material,
- \( R_1 \) is the radius of curvature of the first surface,
- \( R_2 \) is the radius of curvature of the second surface.

For an equiconvex lens:
- Let \( R_1 = R \) (for the first surface),
- Let \( R_2 = -R \) (for the second surface, as per the sign convention).

### Step 4: Substitute Values into the Formula
Substituting these values into the lensmaker's formula:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R} - \left(-\frac{1}{R}\right) \right) \]
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R} + \frac{1}{R} \right) \]
\[ \frac{1}{f} = (\mu - 1) \left( \frac{2}{R} \right) \]

### Step 5: Substitute the Refractive Index
Assuming the refractive index \( \mu = 1.5 \):
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{2}{R} \right) \]
\[ \frac{1}{f} = 0.5 \left( \frac{2}{R} \right) \]
\[ \frac{1}{f} = \frac{1}{R} \]

### Step 6: Solve for Focal Length
Taking the reciprocal gives:
\[ f = R \]
This confirms that the focal length of the equiconvex lens is indeed equal to the radius of curvature of either face.

### Conclusion
Thus, both the assertion and the reason are true, but the reason does not correctly explain the assertion. The correct explanation is derived from the lensmaker's formula.

### Final Answer
- **Assertion**: True
- **Reason**: True, but not the correct explanation for the assertion.

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