A convex lens of focal length `25 cm` is placed co-axially in contact with a concave lens of focal length `20 cm`. Determine the power of the combination. Will the system be converging or diverging in nature ?

Explanation

We have focal length of convex lens,
`f_(1) = + 25 cm = +0.25 m" and focal length of concave lens " f_(2) = -20 cm = - 0.20 m. `
Equivalent focal length,
`(1)/(F) = (1)/(f_(1))+(1)/(f_(2)) = (1)/(25) +(1)/(-20)= (-1)/(100)`
`therefore F= -100 cm`
Power of convex lens, `P_(1)=(1)/(f_(1)) =(1)/(0.25)`
Power of concave lens, `P_(2) =(1)/(f_(2)) =(1)/( -0.20)`
Power of the combination,
`P=P_(1)+P_(2)=(1)/(0.25)+(1)/(-0.20) =(100)/(25) -(100)/(20)rArr (400-500)/(100)=(-100)/(100)=-1D.`
The focal length of the combination = -1m.
As the focal length of the negative, the system will be diverging in nature.