Question

A thin concave and a tin convex lens are in contact. The ratio of the magnitude of power of two lenses is $2/3$ and focal length of combination is $30cm,$ then the focal length of individual lenses are

• A. $-15cm,10cm$
• B. $-75cm,50cm$
• C. $75cm,-50cm$
• D. $75cm,50cm$

Answer 1

The correct option is A $-15cm,10cm$

$\frac{|P_1|}{|P_2|}=\frac{2}{3}\Rightarrow \frac{f_2}{f_1}=\frac{2}{3}...\left(i\right)$
Focal length of their combination, $\frac{1}{f}=\frac{1}{f_1}-\frac{1}{f_2}$
$\Rightarrow \frac{1}{30}=\frac{1}{f_1}-\frac{1\times 3}{2f_1}$ [from (i)]
$\Rightarrow \frac{1}{30}=\frac{1}{f_1}[1-\frac{3}{2}]=\frac{1}{f_1}\times (-\frac{1}{2})$
$\therefore f_1=-15cm$
$\therefore f_2=\frac{2}{3}\times f_1=\frac{2}{3}\times 15=10cm$.