An astronomical telescope consisting of an objective of focal length 60cm and eyepiece of focal length 3cm is focused on the moon so that the final image is formed at least distance of distinct vision, i.e., 25cm from the eye- piece. Assuming the angular diameter of moon (1//2)^@ as the objective, calculate (a) angular size and (b) linear size of image seen through the telescope.

An astronomical telescope consisting of an objective of focal length 6

1.	An astronomical telescope consisting of an objective of focal length 60cm and eyepiece of focal length 3cm is focused on the moon so that the final image is formed at least distance of distinct vision, i.e., 25cm from the eye- piece. Assuming the angular diameter of moon (1//2)^@ as the objective, calculate (a) angular size and (b) linear size of image seen through the telescope.
Answer» SOLUTION :As final image is at LEAST distance of distinct VISION `\|M\|=f_0/f_e[1+f_e/D]=60/3[1+3/25]=22.4` Now as by definition `M=(theta/theta_0)` so the angular SIZE of image `theta= M times theta_c= 22.4 times [1/2]^@=11.2^@=pi/180^@ times 11.2 =0.2 rad` And if I is the size of final image which is at least distance of distinct vision, `theta=(I/25)i.e., I=25 times theta= 25 times 0.2=5cm`