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प्रश्न
Define power of a lens. Write its units. Deduce the relation `1/f =1/f_1 +1/f_2`for two thin lenses kept in contact coaxially.
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उत्तर
Consider two lenses A and B of focal length f1 and f2 placed in contact with each other. An object is placed at a point O beyond the focus of the first lens A. The first lens produces an image at I1 (real image), which serves as a virtual object for the second lens B, producing the final image at I.
Since the lenses are thin, we assume the optical centers (P) of the lenses to be co-incident. For the image formed by the first lens A, we obtain
`1/v_1 -1/u =1/f_1 ........ (1)`
For the image formed by the second lens B, we obtain
`1/v -1/v_1 =1/f_2 ........ (2)`
Adding equations (1) and (2), we obtain
`1/v -1/u =1/f_1 + 1/f_2 ........ (3)`
If the two lens system is regarded as equivalent to a single lens of focal length f, we have
`1/v -1/u =1/f_1 ........ (4)`
From equations (3) and (4), we obtain
`1/f_1 + 1/f_2 =1/f_1 `
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