Question

In a microscope, the focal lengths of two lenses are $1.5\text{cm}$ and $6.25\text{cm}.$ If an object is placed at $2\text{cm}$ from objective and final image is formed at $25\text{cm}$ from eye-lens, the distance between two lenses is -

• A. $6\text{cm}$
• B. $7.75\text{cm}$
• C. $9.25\text{cm}$
• D. $11\text{cm}$

Answer 1

The correct option is D $11\text{cm}$

Given,

$f_0=1.5\text{cm};f_e=6.25\text{cm}{u}_0=-2\text{cm};v_e=25\text{m}$

For the objective lens, using lens formula,

$\frac{1}{v_0}-\frac{1}{u_0}=\frac{1}{f_0}$

$\frac{1}{v_0}=\frac{1}{1.5}-\frac{1}{2}$

$v_0=6\text{cm}$

Using, the relation for the length of the tube, we get

$L=v_0+\frac{D\times f_e}{D+f_e}$

$L=6+\frac{25\times 6.25}{25+6.25}=11\text{cm}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.