Question

The simple microscope having a lens of focal length 5 cm gives the magnification of (least distance of distinct vision \(= 25\) cm)

• A. 5
• B. 6
• C. 4
• D. 10
• E. 12

Hint:

For a simple microscope, magnification is higher when the image is at the near point (\(1 + D/f\)) than when at infinity (\(D/f\)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A simple microscope (or a magnifying glass) uses a single convex lens to produce a magnified virtual image of a small object. The magnification depends on where the final image is formed. The question specifies the case where the image is formed at the least distance of distinct vision (\(D\)), which is the near point of the eye. This provides the maximum angular magnification.
Step 2: Key Formula or Approach:
The formula for the magnifying power (\(M\)) of a simple microscope when the final image is formed at the least distance of distinct vision (\(D\)) is:
\[ M = 1 + \frac{D}{f} \] where \(f\) is the focal length of the convex lens.
Step 2: Detailed Explanation:
We are given the following values:
- Focal length of the lens, \(f = 5\) cm.
- Least distance of distinct vision, \(D = 25\) cm.
Now, we substitute these values into the formula:
\[ M = 1 + \frac{25 \, \text{cm}}{5 \, \text{cm}} \] \[ M = 1 + 5 \] \[ M = 6 \] Step 3: Final Answer:
The magnification of the simple microscope is 6, which corresponds to option (B).