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Derive the equation for effective focal length for lenses in out of contact.

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Consider a two lenses of focal length f1 and f2 arranged coaxially but separated by a distance d can be considered. For a parallel ray that falls on the arrangement, the two lenses produce deviations δ1 and δ2 respectively and The net deviation δ is,

δ = δ1 + δ2 ……. (1)

From Angle of deviation in lens equation, δ  = \(\frac{h}{f}\)

δ1\(\frac{h_1}{f_1}\); δ \(\frac{h_2}{f_2}\);  δ= \(\frac{h_1}{f}\) ..... (2)

The equation (1) becomes,

Substituting the above equation in Equation (3)

The above equation could be used to find the equivalent focal length.

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