Question

Under what conditions in Telescope does the brightness of an image increase M-times?
(A) \[\dfrac{{{F_{objective}}}}{{{F_{eyepiece}}}} = \dfrac{D}{d}\]
(B) \[\dfrac{{{F_{objective}}}}{{{F_{eyepiece}}}} + \dfrac{D}{d}\]
(C) \[\dfrac{{F\left( {f + D} \right)}}{{fd}} + \dfrac{D}{d}\]
(D) None of these

Answer 1

Hint: Telescope aperture tells us about the total amount of light that the telescope can gather. If the aperture is more then it will gather more light.If we want to increase the brightness of the telescope then we have to increase the focal length of the earpiece.

Complete step by step answer:
There are two conditions for getting larger magnification-
Focal length of the objective lens (\[{F_o}\]) should be large.
Focal length of the eye lens (\[{F_e}\]) should be small.
For viewing a clear image through the eyepiece, focal length of the eyepiece should be adjusted in such a way that maximum light passes through it. If we are increasing the brightness, it means we are increasing the focal length.
So, Magnification of telescope,
\[M = \dfrac{{{F_{objective}}}}{{{F_{eyepiece}}}} = \dfrac{D}{d}\]

So, the correct answer is “Option A”.

Note:
A telescope is an optical instrument which uses lenses and mirrors to observe the far distant objects. It can capture more light than the eye but it can also magnify the image. Brightness of the image depends on how much the area in which image light is spreaded. Magnification can be increased by shortening the focal length of the eyepiece. As we have seen that the magnification is inversely proportional to the focal length of the eyepiece and if the lens is of greater aperture then the telescope can gather more light.