Step 1: Understanding the Concept:
A simple microscope consists of a single biconvex lens used to produce an enlarged, upright, virtual image of a small object placed within its focal length. The magnifying power ($m$) measures how much larger the image appears to the human eye compared to viewing the object at the standard near point of distinct vision ($D$) without assistance.
Step 2: Key Formula or Approach:
The magnifying power ($m$) of a simple microscope is mathematically defined for two standard viewing conditions:
1. When the final image is formed at the near point (least distance of distinct vision, $D = 25\text{ cm}$):
$$ m = 1 + \frac{D}{f} $$
2. When the final image is formed at infinity (relaxed eye condition):
$$ m = \frac{D}{f} $$
In both mathematical formulas, $f$ represents the focal length of the convex lens.
Step 3: Detailed Explanation:
Let's analyze the mathematical relationship between the magnifying power ($m$) and the focal length ($f$):
From both baseline equations, it is clear that the magnifying power is inversely proportional to the focal length of the lens:
$$ m \propto \frac{1}{f} $$
This inverse relationship tells us that:
- If the focal length ($f$) increases, the magnifying power ($m$) decreases.
- If the focal length ($f$) decreases, the value of the fraction $\frac{D}{f}$ grows larger, causing the overall magnifying power ($m$) to increase.
The aperture or the mechanical physical radius of the outer rim of the lens alters the light-gathering capacity and brightness of the image, but it has no direct mathematical influence on the geometric magnifying power. Therefore, decreasing the focal length is the correct mechanism to boost magnification. This tracks with option (B).
Step 4: Final Answer:
The magnifying power increases when the focal length decreases.