Question

(i) Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main consideration required in selection the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.

(ii) A compound microscope has an objective of focal length 1.25 cm and eyepiece of focal length 5 cm. a small object is kept as 2.5 cm from the objective. If the final image formed is at infinity, find the distance between the objective and the eyepiece.

Answer 1

(i)

For a large magnifying power, f_o should be large and f_e should be small.

For a higher resolution, the diameter of the objective should be large.

Note for students: You may draw refractive or reflective telescope.

(ii) \(\frac{1}{v_o}-\frac{1}{u_o}=\frac{1}{f_o}\)

\(\frac{1}{v_o}=\frac{1}{f_o}+\frac{1}{u_o}\)

\(\frac{1}{v_o}=\frac{1}{1.25}-\frac{1}{2.5}\)

\(\frac{1}{v_o}=\frac{1}{2.5}⇒v_o=2.5cm\)

If the final image is at infinity it means image from objective lens would be at focal length of eye piece.

Additionally, this is 2.5 cm away from objective lens.

Hence tube length in this case = 2.5 cm + 5.0 cm = 7.5 cm