Question

Focal length of converging combination of two lens is 20 cm. The ratio of dispersive power is 2:3. One of the focal length will be:

• A. 33.33 cm
• B. -10 cm
• C. -15 cm
• D. 20 cm

Answer 1

The correct option is A 33.33 cm

Given,

$P_1:P_2=2:3$

$f=+20cm$

Lets consider the dispersive power of the lens is $x$.

The power of the combination of two converging lens is given by

$P=P_1+P_2$

$\frac{1}{f}=2x+3x=5x$

$x=\frac{1}{5\times 20}=\frac{1}{100}$

The Power of lens 1 is $2x=\frac{1}{f_1}$

$\frac{1}{f_1}=2\times \frac{1}{100}$

$f_1=50cm$

The power of lens 2

$\frac{1}{f_2}=3x=3\times \frac{1}{100}$

$f_2=33.33cm$

The correct option is not given.