Question

Suppose you are using a telescope to look at birds in a distant nest. You then look through it at birds in a nest that is four times as far away. If you want the birds in the more distant nest to appear the same size in your telescope as the closer birds, how would you adjust your telescope? Your original telescope has objective focal length fo and eyepiece focal length fe.

a. replace the objective lens with one that has focal length 4fo and keep the length of the telescope the same
b. replace the objective lens with one that has focal length 16fo and increase the length of the telescope
c. replace the objective lens with one that has focal length 4fo and increase the length of the telescope
d. replace the eyepiece with one that has focal length 4fe and keep the length of the telescope the same
f. replace the objective lens with one that has focal length 16fo and keep the length of the telescope the same

Answer 1

To make distant birds appear the same size as closer ones in a telescope, replace the objective lens with one having a focal length of 4fo and increase the length of the telescope accordingly. Option number C is correct.

Step-by-step explanation:

If you want the birds in a more distant nest to appear the same size in your telescope as the closer birds, you would need to increase the focal length of the objective lens because the magnification provided by a telescope is directly related to the focal lengths of its lenses. The angular magnification (M) is defined as the ratio (M = 0'/0) and can be represented by the equation (M = fo/fe), where (fo) is the focal length of the objective lens and (fe) is the focal length of the eyepiece.

Since the second nest is four times further away, to achieve the same perceived size, you would need to increase the focal length of the objective lens by a factor of four. Therefore, the correct adjustment would be to replace the objective lens with one that has a focal length of (4fo) and increase the length of the telescope to accommodate the new lens size. This is because the telescope's length must be slightly less than the sum of the focal lengths of the lenses to produce a properly focused image.