Question

The focal lengths of the objective and eyepiece of a compound microscope are 2 cm and 3 cm respectively. The distance between the objective and eye-piece is 15 cm. The final image formed is at infinity. The distances in cm of object and image from objective are going to be then:

• A. 2.4 and 12
• B. 2.4 and 15
• C. 2.3 and 3.0
• D. 2.3 and 12

Answer 1

Answer: (A)

2.4 and 12

According to the question final image is formed at infinity.

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

Applying lens image formation on objective lens,

$\frac{1}{2}=\frac{1}{12}-\frac{1}{x}$

$\frac{1}{x}=\frac{1}{12}-\frac{1}{2}=\frac{-5}{12}$

$x=-2.4cm$, -ve indicates distance is towards left side of lens.

Thus, the option (A) $2.4and12cm$ is correct.