Question

Imagine you have two converging lenses. Lens A has a focal length of 12.5 cm. Lens B has a focal length of 50.0 cm. The diameter of each lens is 6.50 cm. Assume a near point of 25.0 cm.

a)     How could you make a microscope with 4x magnification using these lenses?

b)     How could you make a telescope with 4x magnification using these lenses?

c)     Which of these is more practical? Why?

Answer 1

a) Let , Focal length of lens A be f_a = 12.5 cm

Focal length of lens B be f_b = 50.0 cm

Tube lenght of microscope = s (s is also approximate distance between two lenses)

For microscope, we choose f_a to be objective lens and f_b to be eyepiece. (Reason is quite simple we want object to be closer to microscope, so it can gather more light from object.)

Magnification of microscope M = m.m_o (m = Lateral magnification of objective, m₀ = Angular magnification of eyepiece)

m = (i / p) (i = image distance, p = object distance)

In microscope , object is close to focal length of Objective , p = f_a  and image distance is approximated to i = s (s = tube length )

m = (s / f_a)

m_o = (25cm / f_b)

  

s = 100 cm

Thus by keeping tube lenght 100 cm, 4x magnification can be achieved.

b) For refracting telescope , we keep f_b to be objective and f_a to be eyepiece.

Magnification of telescope M = -(f_b / f_a)

= -(50.0 / 12.5)

M = 4

Keeping larger focal length lens as objective , we can make telescope.

c) Making Telescope is more practical than microscope.

Only bcoz tube lenght of s = 100 cm = 1m is too long for practical microscope.