1. Understand the simple microscope

A simple microscope is a convex lens used to view a small object placed close to the lens, producing a virtual, erect, magnified image.

The angular magnification of a simple microscope is defined as $M = \frac{\text{angle subtended by image at eye}}{\text{angle subtended by object at unaided eye at least distance of distinct vision}}.$

So, in a microscope, magnification is about increasing angular size.

2. Check Assertion A

Assertion A says:

For a simple microscope, the angular size of the object equals the angular size of the image.

This is false.

For a magnifying device, the whole purpose is that the image subtends a larger angle at the eye than the object would subtend when viewed directly at the least distance of distinct vision.

If angular sizes were equal, there would be no magnification.

Hence, $\theta_i \neq \theta_o,$ and in fact for magnification, $\theta_i > \theta_o.$

So, Assertion A is false.

3. Check Reason R

Reason R says:

Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle.

This is true in essence.

A simple microscope allows the object to be placed closer than the normal least distance of distinct vision ($25\,\text{cm}$), while still forming a clear virtual image. Because the object is effectively viewed under a larger angle, the image appears magnified.

Thus, Reason R is true.

4. Choose the correct option

• Assertion A: False
• Reason R: True

Therefore, the correct option is:

$\boxed{\text{B: A is false but R is true}}$

5. Compare with stored correct answer

Stored correct answer = C

My derived answer = B

These do not match.

The stored answer seems incorrect because in a simple microscope, angular magnification means the angle subtended by the image is greater than that subtended by direct viewing of the object, not equal.