The power and aperture of lenses $L_1, L_2$ and $L_3$ are given below in tabular format. Which pair of lenses should be chosen for constructing a microscope?
|
Lens |
Power |
Aperture |
|
$L_1$ |
3 D |
8 cm |
|
$L_2$ |
6 D |
1 cm |
|
$L_3$ |
10 D |
1 cm |
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $L_2$ as eyepiece and $L_3$ as objective
Objective lens should have high power and small focal length, eyepiece should have lower power (larger focal length) than objective.
Given:
L1: Power = 3 D, Aperture = 8 cm
L2: Power = 6 D, Aperture = 1 cm
L3: Power = 10 D, Aperture = 1 cm
Focal length: f = $\frac{100}{P}$ (cm, P in D)
$f_{L1} = \frac{100}{3} \approx 33.33 \text{ cm}$
$f_{L2} = \frac{100}{6} \approx 16.67 \text{ cm}$
$f_{L3} = \frac{100}{10} = 10 \text{ cm}$
Objective: L3 (shortest focal length)
Eyepiece: L2 (longer focal length, suitable aperture)
Answer: L2 as eyepiece and L3 as objective.