A convex lens and concave lens of focal length +20 cm and -30 cm respectively . Then find the power of each lens. Find the focal length of combined lens. And find the combined power of the lenses (+5D,-3.3D, +60 cm , + 1.7 D)

Explanation

Given the focal lengths as follows `f_(1) =+20 cm, f_(2)=-30 `cm
`P_(1) =(100)/(f_(1)) ("in cm") =(100)/(20)=5D`
`P_(2)=(100)/(f_(2))` (in cm) `=(100)/(-30)=-3.3D`
Combined focal length `implies 1/f=1/f_(1) + 1/f_(2)`
`implies 1/f= 1/(20) -(1)/(30)`
`implies 1/f =(30-20)/(600)`
`implies 1/f =(30-20)/(600)`
`implies 1/f =(1cancel(0))/(60cancel0)=(1)/(60)`
`implies f=+60cm`
Result power `P=P_(1) +P_(2) =5-3.3 =1.7 D`