In a two-lens system, the image produced by one lens acts as the object for the

Question

In a two-lens system, the image produced by one lens acts as the object for the next lens. This simple principle finds applications in many optical instruments, including some of common use such as the microscope and the telescope.

The microscope available in your biology lab has a converging lens (the eyepiece) with a focal length of 2.50 cm mounted on one end of a tube of adjustable length. At the other end is another converging lens (the objective) that has a focal length of 1.00 cm . When you place the sample to be examined at a distance of 1.30 cmfrom the objective, at what length l will you need to adjust the tube of the microscope in order to view the sample in focus with a completely relaxed eye?

Explanation / Answer

The image distance for the objective which is given by,

1 / d0 + 1 / di = 1 / f

where, d0 = object distance = 1.3 cm

f = objective focal length = 1 cm

then, we get

1 / di = 1 / (1 cm) - 1 / (1.3 cm)

di = 4.33 cm

The object distance for eye-piece, given that it forms an image at infinity & its focal length is 2.5 cm which will be :

do,e = fe

The length of a tube will be given as :

using a formula, we have

L = di + fe = [(4.33 cm) + (2.5 cm)]

L = 6.83 cm

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