Question

Why is a reflecting telescope superior in comparison to a refracting telescope? Write two reasons.
The magnifying power of a telescope is 8. When it is adjusted for parallel rays the distance between the eyepiece and objective lens is 18 cm. Determine the focal length of both lenses.

Answer 1

Hint: Magnifying power of a telescope is the ratio of the angle subtended at the eye of the telescope by the image at least distance of distinct vision to the angle subtended at the eye by the object lying at infinity.
The eyepiece is the lens in the telescope that a person looks into and the objective lens is the lens of the telescope that is close to the object.

Complete step by step solution:
Step I:
Reflecting telescope is superior to refracting telescope because
Reflecting telescopes do not suffer too much from chronic aberrations.
Reflecting telescopes should have only one side polished as incident light reflects from the mirror rather than passing through it.
Step II:
Given magnifying power is 8. Magnifying power of a telescope is given by
\[M = - \dfrac{{{f_o}}}{{{f_e}}}\]
\[\Rightarrow 8 = - \dfrac{{{f_o}}}{{{f_e}}}\]
\[\Rightarrow {f_o} = - 8{f_e}\]---(i)
Step III:
Distance between eyepiece and objective lens is
\[L = \left| {{f_o}} \right| + \left| {{f_e}} \right|\]
\[\Rightarrow 18 = 8{f_e} + {f_e}\]
\[\Rightarrow 18 = 9{f_e}\]
\[\Rightarrow {f_e} = \dfrac{{18}}{9} = 2cm\]
Step IV:
Substitute value of \[{f_e}\]in equation (i),
\[{f_o} = - 8 \times 2 = - 16cm\]

$\therefore$ The Focal length of objective lens is = -16cm. The Focal length of the eyepiece lens is = 2cm.

Note:
Chronic aberrations in the telescope is a type of failure of lens used in the telescope. In this defect, the lens is not able to focus on all the colors to the same point. It is caused by the dispersion of light. The refractive index of the lens varies with the wavelength of the lights as different wavelengths have different focal lengths. As a result, they do not focus at the same point. In order to avoid chronic aberrations, lenses made up of low dispersion glasses should be used.