Question

Consider lenses L₁, L₂ and L₃ as specified in the following table. Which of them will you select as objective and eyepiece for constructing best possible

1. telescope
2. compound microscope?

Give reason for your answer.

Lens	L1	L2	L3
Power	6 D	3 D	10 D
Aperture	1 cm	8 cm	1 cm

Answer 1

To construct the best possible telescope and compound microscope, we first need to determine the focal lengths of the given lenses using the formula f = `1/P` (where P is the power in Dioptres and f is the focal length in meters.)

Lens	L1	L2	L3
Power (P)	6 D	3 D	10 D
Aperture (A)	1 cm	8 cm	1 cm
Focal length (f)	`1/6` m ≈ 16.7 cm	`1/3` m ≈ 33.3 cm	`1/10` m = 10.0 cm

i. Objective: L₂

Eyepiece: L₃

An astronomical telescope requires an objective with a large focal length (f₀) and a large aperture. A large focal length increases the magnifying power `(M = f_0/f_e)`, and a large aperture (8 cm) allows more light to enter, creating a brighter image of distant objects. The eyepiece should have a small focal length to further increase magnification.

ii. Objective: L₃

Eyepiece: L₁

In a compound microscope, the objective should have a very small focal length (f₀) and a small aperture to produce a highly magnified real image. L₃ has the smallest focal length (10 cm). The eyepiece should have a comparatively larger focal length (f_e) than the objective to facilitate comfortable viewing and high total magnification `(M approx L/f_0 * D/f_e)`. Therefore, L₁ (16.7 cm) is the best fit for the eyepiece.