Question

An angular magnification of 30 is desired using an objective of focal length 1.25 cm and eye-piece of focal length 5.0 cm. To set up the microscope the distance between the lenses is :

• A. 3.6 cm
• B. 6.6 cm
• C. 13.75 cm
• D. 7.75 cm

Answer 1

The correct option is C 13.75 cm

$\begin{array}{c}\text{given}m=30\\ f_0=1.25cm\\ f_e=5cm\end{array}$

$\begin{array}{c}\text{We know that}\\ \begin{array}{c}m=m_0\text{me}(⋮m_e=\frac{D}{fe})\\ 30=m_0\times \left(\frac{D}{fe}\right)\end{array}\end{array}$

$\begin{array}{c}{m}_0=\frac{30\times 5}{25}\\ m_0=6cm\\ m_e=5cm\end{array}$

$\begin{array}{cc}{m}_0=\frac{v_0}{u}& \Rightarrow v_0=6u\\ \frac{1}{f}& =\frac{1}{v}+\frac{1}{u}\\ \frac{1}{1.2s}& =\frac{1}{v}+\frac{1}{u}\Rightarrow \frac{4}{5}=\frac{7}{v_0}\end{array}$

$\begin{array}{cc}{V}_0& =\frac{35}{4}cm.\\ \text{Lenth}& =V_0+f_e\\ & =13.75\end{array}$