Two plano-convex thin glass lenses are brought into contact with their spherical surfaces. Find the optical power of such a system if in reflected light with wavelength `lambda = 0.60 mu m` the diameter of the fifth bringht ring is `d = 1.50 mm`.

Explanation

Path difference between waves reflected by the two convex surface is
`r^(2) ((1)/(R_(1)) + (1)/(R_(2)))`
Taking account of the phase change at the `2^(nd)` surface we write the condition of bright rings as
`r^(2) ((1)/(R_(1)) + (1)/(R_(2))) = (2k + 1)/(1) lambda`
`k = 4` for the fifth brighr ring.

Thus `(1)/(R_(1)) + (1)/(R_(2)) = (9)/(2)lambda.(4)/(d^(2)) = (18 lambda)/(d^(2))`
now `(1)/(f_(1)) = (n - 1) (1)/(R_(1)), (1)/(f_(2)) = (n - 1) (1)/(R_(2))`
so `(1)/(f) = (1)/(f_(1)) + (1)/(f_(2)) = (n - 1) (18 lambda)/(d^(2)) = Phi = 2.40D`
Here `n = R.I.` of glass `= 1.5`.