Question

The focal lengths of the objective and the eyepiece of a compound microscope are 2.0 cm and 3.0 cm respectively. The distance between the objective and the eyepiece is 15.0 cm. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance, in cm, of the object and the image produced by the objective, measured from the objective lens, are respectively

Answer 1

According to the question the final image is formed at infinity.

The object for eyepiece (image formed by objective lens) should be at a distance of f = 3 cm from it.

Hence distance of the image formed by the objective lens from the objective lens is 15 − 3 = 12 cm

Using lens formula for the objective lens,

\(\frac 1f = \frac 1v - \frac 1u\)

\(\frac 12 = \frac 1{12} - \frac 1x\)

x = −2.4 cm

-ve indicates distance is towards left of the lens.