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Question
An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?
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Solution
Thin lens formula: `1/v - 1/u = 1/f`
For a given object position if focal length of the lens does not change, the image position remains unchanged.
By lens maker's formula,
`1/f = (mu - 1) (1/R_1 - 1/R_2)`
For this position R1 is positive
And R2 is negative. Hence focal length at this position
`1/f_1 = (mu - 1) (1/((+ R_1)) - 1/((-R_2))) = (mu - 1)(1/R_1 + 1/R_2)`
Now the lens is reversed,
At this position R2 is positive and R1 is negative. Hence focal length at this position is
`1/f_2 = (mu - 1) (1/((+ R_2)) - 1/((-R_1))) = (mu - 1)(1/R_1 + 1/R_2)`
We can observe the focal length of the lens does not change in both positions, hence the image position remains unchanged.
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