1.

A beam of light converges to a point `P`. A lens is placed in the path of the covergent beam `12 cm` from `P`. At what point does the beam converge if the lens is (a) a convex lens of focal length `20 cm` (b) a concave lens of focal length `16 cm` ?

Answer» Here, the point `P` on the right the lens acts as a virtual object, `:. u = 12 cm, v = ?`
(a) `f = 20 cm`
As `(1)/(v)-(1)/(u)=(1)/(f) :. (1)/(v)-(1)/(12)=(1)/(20)`
`(1)/(v)=(1)/(20)+(1)/(12)=(3 + 5)/(60) = (8)/(60)`
`v = 60//8 = 7.5 cm`
Image is at `7.5 cm` to the right of the lens where the beam converges.
(b) `f = -16 cm, u = 12 cm, :. (1)/(v)=(1)/(f)+(1)/(u)=-(1)/(16)+(1)/(12)=( - 3 + 4)/(48) = (1)/(48)`
`v = 48 cm`
Hence, image is at `48 cm`. to the right of the lens, where the beam would converge.


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