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in Optics by (15 points)
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1/f = (u-1) [ 1/R1- 1/R2 ] where the symbol have their usual meanings . State the assumption used and the convention of signs used.

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Let the distance of object O from the lens is a image I1 is a distance v1, image I at distance v

From first surface AB image of O get on I1

\(\frac{\mu -1}{R_1} = \frac{\mu}{v_1} - \frac 1u\)   ......(i)

From second surface CD image of I1 get

\(\frac{\frac 1\mu -1}{R_2} = \frac{\frac 1\mu -1}v - \frac 1{v_1}\)   ......(ii)

\(\mu = \frac 1u, u = v_1\) for CD surface light ray passing from denser to rarer medium.

Equation (2) multiply by \(\mu\)

\(\frac 1v - \frac \mu{v_1} = - \frac{1 - \mu}{R_2}\)    .....(iii)

adding equation (i) + (iii),

\(\frac 1v -\frac 1u = \frac{\mu -1}{R_1} + \frac{1-\mu}{R_2}\) 

if \(u =\infty\)

\(v = f\)    ......(iv)

\(\frac 1f = (\mu - 1)(\frac 1{R_1} - \frac 1{R_2})\)   ......(v)

By comparing equation (iv) and (v)

\(\frac 1f = \frac 1v - \frac 1u\)

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