Question

A compound microscope has an objective of focal length 1.25 cm and eyepiece of focal length 5 cm. A small object is kept at 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

Distance between the objective and the eyepiece, L =

\[v_0 + \left| u_e \right|\]

To find v₀, we have:

\[u_0 = - 2 . 5 \text {cm and } f_0 = 1 . 25 cm\]

\[\text { Now }, - \frac{1}{u_0} + \frac{1}{v_0} = \frac{1}{f_0}\] \[or \ v_0 = 2 . 5 cm\]

To find u_e, we have:

\[v_e = \infty\text { and } f_e = 5 cm\]

Calculating using the same formula as above, we get:

\[u_e = - 5 cm\]

∴ L = 2.5 + 5 = 7.5 cm