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Find the poistions of the principle plan...

Find the poistions of the principle planes, the focal length and the sign of the optical power of a thick convex-concave glass lens
(a) whose thickness is equal to `d` and curvature radii of the surfaces are the same and equal to `R`,
(b) whose refractive surfaces are concentric and have the curvarure radii `R_(1)` and `R_(2) (R_(2) gt R_(1))`.

Text Solution

Verified by Experts

The power of the lens is (as in the pervious problem)
`Phi = (n - 1)/(R ) - (n -1)/(R ) - (d)/(n) ((n -1)/(R )) (-(n - 1)/(R )) = (d(n - 1)^(2))/(nR^(2)) gt 0`.
The principle planes are located on the side of the convex surface at a distance `d` from each other, with the front principle plane being removed from the conve surfcae of the lens by a distance `R//(n - 1)`.
(a) Here `Phi = -(n - 1)/(R_(1)) + (n + 1)/(R_(2)) + (R_(2) - R_(1))/(n) ((n -1)^(2))/(R_(1)R_(2))`
`= ((n - 1)(R_(2) - R_(1)))/(R_(2)R_(1)) [-1 + (n -1)/(n)]`
`=- (n -1)/(n) ((1)/(R_(1)) - (1)/(R_(2))) lt 0`
Both principle planes pass through the common centre of curvature of the surfcaes of the lens.
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