A combination of lenses for a camera contains two converging lenses of focal lengths 20 cm and 40 cm and a diverging lens of focal length 50 cm. Find the power and focal length of the combination.A optical instrument in which the above arrangement of convex lens is used is a convex lens used to burn paper by focusing sunlight.

#### Solution

Focal length (f_{1}) of the 1^{st} converging lens = 20 cm = 0.2 m

Focal length (f_{2}) of the 2^{nd} converging lens = 40 cm = 0.4 m

Focal length (f_{3}) of the diverging lens = -50 cm = -0.5 m (negative sign due to sign convention)

Power = `1/"foccal length of lens (in metre)"`

Power *(**P*_{1}) of 1^{st} lens = `1/0.2=2.5D`

power (*P*_{2}) of 2^{nd} lens = `1/0.4=2.5 D`

Power (*P*_{3}) of diverging^{ } lens =`1/0.5 =-2D`

Net power of the combination = *P*_{1} + *P _{2}*+

*P*= 5 + 2.5 + (-2) = 5.5 D

_{3}Net focal length of the combination = `1/"net power"=1/5.5=0.1818m=18.18 cm`