Question

After taking an astronomy class, you purchase an astronomical telescope that has a focal length for the objective and eyepiece respectively of 196 cm and 1.27 cm. After using the telescope several times, you decide to increase its angular magnification by replacing the eyepiece. After replacing the eyepiece, the length of the barrel must be adjusted in order to bring objects into focus. Determine the best angular magnification you can obtain, if the barrel can only be shortened by 0.54 cm from its current length.
  

Answer 1

L = f_o + f_e

where L is barrel length

we are given

f_o = 196 cm and f_e = 1.27 cm

so,

L = 197.27 cm

Now, if we shorten the barrel length by 0.54 cm

then new L = 197.27 - 0.54 = 196.73

we find eyepiece focal length using this

note that objective focal length does not change

so,

f_e = 196.73 - 196 = 0.73 cm

so

angular magnification = 196 / 0.73 = 268.5

This is the maximum magnification he can get. If he decreases the length of barrel by less than 0.54 cm then angular magnification will also decrease.