Question

A simple microscope is a combination of two lenses in contact. Their powers are \(+20\text{D}\) and \(-4\text{D}\). The distance of distinct vision is \(25 \text{cm}\). When seen through the microscope, the size of the image of an object \(3 \text{mm}\) high is

• A. \(1.8 \text{cm}\)
• B. \(1.5 \text{cm}\)
• C. \(1.2 \text{cm}\)
• D. \(0.6 \text{cm}\)

Hint:

Add the powers to find the focal length, then use m = 1 + D/f for the image at the near point.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Two thin lenses in contact have a combined power equal to the sum: \(P = P_1 + P_2\). A simple microscope used with the image at the least distance of distinct vision has magnification \(m = 1 + \frac Df\).

Step 2: Key Formula or Approach:
\(P = 20 - 4 = 16\) D, so \(f = \frac{1}{16}\ \text{m} = 6.25\) cm.

Step 3: Detailed Explanation:
\[ m = 1 + \frac{25}{6.25} = 1 + 4 = 5 \]
Image size \(= 5 \times 3\ \text{mm} = 15\ \text{mm} = 1.5\ \text{cm}\).
The value \(1.8\) cm would need \(m = 6\), that is \(f = 5\) cm, which does not match the combined power of \(16\) D.

Final Answer:
The image is \(1.5\) cm high, option (B). \[ \boxed{1.5\ \text{cm}} \]