Question

An opera glass has a length of $30$ cm and its magnifying power is $5$ when used to view distant objects. Calculate the focal length of its lenses.

• A. $5$cm and $25$cm
• B. $7$cm and $35$cm
• C. $6$cm and $30$cm
• D. $8$cm and $4$cm

Answer 1

The correct option is A $5$cm and $25$cm

For an opera glass

$\begin{array}{c}\text{length}\left(L\right)=f_0+fe\\ \text{magnifying power}=\frac{f_0}{f_e}\end{array}$

where fo = focal length of objective lens.

fe = focal length of eye piece.

Here

$\begin{array}{cc}{f}_0+f_e& =30\to 1\\ \frac{f_0}{f_e}& =5\Rightarrow f_0=5f_e\to 2\end{array}$

substitute equation (2) in (1) .

$\begin{array}{cc}{f}_0+f_e& =30\\ 3f_e+f_e& =30\\ 6f_e& =30\\ F_e& =5cm\end{array}$

By (2)

$\begin{array}{c}{f}_0=5f_e\\ f_0=5\left(5\right)\\ f_0=25cm\end{array}$

so focal length of its lenses $=5cm$ and $=25cm$

Hence option $A$ is correct.