A : The objective and the eye-piece of a compound microscope should have short focal lengths.
R : Magnifying power of a compound microscope is inversely proportional to the focal lengths of both the lenses.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion (A)
The assertion states that "The objective and the eye-piece of a compound microscope should have short focal lengths."

- In a compound microscope, the objective lens is responsible for forming a real, inverted image of the object, which is then magnified by the eyepiece.
- Short focal lengths for both lenses allow for greater magnification, which is essential for observing small details in the specimen.

### Step 2: Understand the Reason (R)
The reason states that "Magnifying power of a compound microscope is inversely proportional to the focal lengths of both the lenses."

- The magnifying power (M) of a compound microscope can be expressed as:
\[ M = \frac{L}{F_O} \times \frac{D}{F_E} \]
where:
- \( L \) = length of the tube,
- \( D \) = distinct vision distance,
- \( F_O \) = focal length of the objective lens,
- \( F_E \) = focal length of the eyepiece.

- From this equation, we can see that the magnifying power \( M \) is directly proportional to \( L \) and \( D \), but inversely proportional to \( F_O \) and \( F_E \). This means that as the focal lengths \( F_O \) and \( F_E \) decrease (i.e., become shorter), the magnifying power \( M \) increases.

### Step 3: Conclusion
Since both the assertion and the reason are correct, and the reason supports the assertion, we can conclude that:

- The assertion (A) is true.
- The reason (R) is true and explains the assertion.

Thus, the correct answer is that both A and R are true, and R is the correct explanation of A.