Question

If the magnitude of dispersive power of two lenses are $0.024$ and $0.036$. There focal length will be for abberation free combination.

• A. $30cm,-40cm$
• B. $30cm,-45cm$
• C. $10cm,30cm$
• D. $20cm,-35cm$

Answer 1

The correct option is B $30cm,-45cm$

$\text{Given - Dispersive power}$

$\begin{array}{c}{\omega }_1=0.024\\ {\omega }_2=0.036\end{array}$

Relation b/w free focal length along with disperse poure

$\begin{array}{c}\frac{f_1}{f_2}=\frac{-{\omega }_1}{{\omega }_2}\\ \Rightarrow \frac{f_1}{f_2}=\frac{-0.024}{0.036}\\ \Rightarrow \frac{f_1}{f_2}=-\frac{2}{3}\end{array}$

Now we can write in terms of $f_1$ and $f_2$ from ophon, $f_1=+30,f_2=45$

$\begin{array}{cc}& \frac{f_L}{f_2}=\frac{-30}{45}\\ \Rightarrow \frac{f_1}{f_2}=& \frac{-2}{3}-\left(11\right)\\ \text{So,}{f}_1=30cm,& f_2=-45cm\end{array}$

(hit and try method)

Hence,(B) is correct option.