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

• A. 2.4 and 12.0
• B. 2.4 and 15.0
• C. 2.0 and 12.0
• D. 2.0 and 3.0

Answer 1

The correct option is A 2.4 and 12.0

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 $f=3\text{cm}$ from it.
Hence distance of the image formed by the objective lens from the objective lens is $15-3=12\text{cm}$
Using lens formula for the objective lens,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{2}=\frac{1}{12}-\frac{1}{x}$
$x=-2.4\text{cm}$
-ve indicates distance is towards left of the lens.