Question

The focal lengths of the objective and the eyepiece of a compound microscope are $2.0\text{cm}$ and $3.0\text{cm}$, respectively. The distance between the objective and the eyepiece is $15.0\text{cm}$. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance, in $\text{cm}$, 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.