Answer to Question #166413 in Optics for Charles

Question

A compound microscope has lenses of focal length 1.0cm and 5.0cm. An object is placed 1.2cm from the objective lens. If a virtual image is formed 25cm from the eyepiece, calculate the distance between the two lenses

Answer 1

Answer

1) Using the lens formula for image q formed by the objective.

$\frac{1}{f_o} =\frac{1}{p}+\frac{1}{q}\\ \frac{1}{1}=\frac{1}{1.2}+\frac{1}{q}\\ q=6 cm.$

2) Now, this image will act as an object for second lens i.e. eyepiece. Using the lens formula for the distance p_1 from the eyepiece.

$\frac{1}{f_e} =\frac{1}{p_1 }+\frac{1}{q_1}\\ \frac{1}{5}=\frac{1}{p_1} +\frac{1}{(-25)}\\ p_1=4.2 cm.$

3) The distance between the two lenses:

$L=6+4.2=10.2 cm.$