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Two identical thick symmetrical biconvex...

Two identical thick symmetrical biconvex lenses are put close together. The thickness of each equals the curvature radius of its surfaces, i.e `d = R = 3.0 cm`. Find the optical power of this system in air.

Text Solution

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Optical powers of the two surfaces of the lens are
`Phi_(1) = (n - 1)//R` and `Phi_(2) = (1 - n)//-R = (n -1)/(R )`
So, the power of the lens of thickness `d`,
`Phi' = Phi_(1) + Phi_(2) - (dPhi_(1)Phi_(2))/(n) = (n - 1)/(R ) + (n -1)/(R ) - (d(n - 1)^(2)//R^(2))/(n^(2)) = (n^(2) - 1)/(nR)`
and optical power of the combination of these two thick lenses,
`Phi = Phi' + Phi' = 2Phi' = (2(n^(2) - 1))/(nR)`
So, power of this system in air is, `Phi_(0) = (Phi)/(n) = (2(n^(2) - 1))/(n^(2)R) = 37D`.
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