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Calculate the positions of the principle...

Calculate the positions of the principle planes and focal points of a thick convex-concave glass lens if the curvature radius of the convex surface is equal to `R_(1) = 10.0 cm` and of the concave surface to `R_(2) = 5.0 cm` and the lens thickness is `d = 3.0 cm`.

Text Solution

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The optical power of first convex surface is,
`Phi = (P(n - 1))/(R_(1)) = 5D`, as `R_(1) = 10 cm`
and the optical power of second concave surface is,
`Phi_(2) = ((1 - n))/(R_(2)) =- 10D`
So, the optical power of the system,
`Phi = Phi_(1) + Phi_(2) -(d)/(n)Phi_(2) =-4D`
Now, the distance of the primary principle plane from the vertex surface is given as,
`x = ((1)/(Phi))((d)/(n)) Phi_(2)`, here `n_(1) = 1` and `n_(2) = n`.
`= (d Phi_(2))/(Phin) = 5cm`
and the distance of secondary principle plane from the vertex of second concave surface,
`x =-((1)/(Phi))((d)/(n)) Phi_(1) =- (d Phi_(1))/(Phi n) = 2.5 cm`
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