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: Combined focal length:
$f = \frac{100}{16} = 6.25$ cm.

Step 2: Magnification and size:
With the image at $25$ cm, $m = 1 + \frac{25}{6.25} = 5$, so the image height is $5 \times 0.3 = 1.5$ cm.

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