#### Question

A convex lens of focal length 25 cm is placed coaxially 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?

#### Solution

We have focal length of convex lens,

`f_1 = +25 cm = +0.25 m`and focal lenghth of conceave

lens, f_{2} =-20 cm =-0.20 m

Equivalent focal length, `f= 1/f_1 +1/f_2 =1/25 +1/-20=-1/100`

∴ F =- 100 cm

Power of convex lens, `P_1 = 1/f_1 = 1/0.25`

Power of convex 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 = (400 - 500)/100 = (-100)/100 = -1D`

**The focal length of the combination =–1 m = –100 cm.**

**As the focal length is in negative, the system will be diverging in nature.**

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Solution A Convex Lens of Focal Length 25 Cm is Placed Coaxially in Contact with a Concave Lens of Focal Length 20 Cm. Determine the Power of the Combination. Concept: Concave Mirror.