A beam of light converges to a point P.A lens is placed in the path of the convergent 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` ?
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Here, the point `P` on the right of the lens acts as a virtual object, `:. U = 12 cm, v = ?` 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 = - 16cm, 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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