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A convex lens of focal length f_(1)is kept in contact with another lens of focal length/2. Find an expression for the focal length of the combination. |
Answer» Solution :Consider TWO THIN lenses A and B of focal LENGTHS `f_(1)` and `f_(2)`placed in contact. Let a point object be placed at O, beyond the focus of first lens A. Lens A forms a REAL image at `I_(1)`. This image serves as a virtual object for second lens B and the final real image is formed at I.  For image `I_(1)` formed by first lens, we have `1/v_(1) -1/u =1/f_(1)` and for the image I formed by the second lens, we have `1/v - 1/v_(1) = 1/f_(2)`...(ii) Adding (i) and (ii), we have `1/v - 1/u =1/f_(1) + 1/f_(2)`...(iii) If the two lens system is considered as equivalent to a single lens of focal length f, then `1/v -1/u = 1/f` COMPARING (iii) and (iv), we find that : `1/f = 1/f_(1) + 1/f_(2)` |
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