Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R: 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. In the light of the above statements, choose the most appropriate answer from the options given below:

In a simple microscope (magnifying glass), a convex lens of short focal length is used. The object is placed between the lens and its focus, and the lens produces a virtual, erect, and magnified image on the same side as the object.

Consider a thin convex lens. When a ray passes through the optical centre of the lens, it goes undeviated. This means that the object and its virtual image subtend the same angle at the optical centre of the lens. Since the eye is placed very close to the lens, the angular size of the object (as seen through the lens) is essentially equal to the angular size of the image. Therefore, Assertion A is true.

Now consider viewing the object without the lens. The closest distance at which the unaided eye can focus is the near point, $$D = 25$$ cm. Without the magnifying glass, the object must be placed at least 25 cm away, where it subtends a small angle $$\alpha_0 \approx \frac{h}{D}$$, with $$h$$ being the object size.

With the magnifying glass, the object can be placed much closer to the eye (between the lens and its focus, at a distance $$u < f$$, which is typically much less than 25 cm). At this closer distance, the object subtends a larger angle $$\alpha \approx \frac{h}{u}$$ at the lens (and hence at the eye). The magnifying power is $$m = \frac{\alpha}{\alpha_0} = \frac{D}{u}$$, which is greater than 1 since $$u < D$$. Therefore, Reason R is true.

Since the magnification arises precisely because the lens allows the object to be placed closer than the near point, thereby subtending a larger angle, Reason R correctly explains Assertion A. Both A and R are true and R is the correct explanation of A.