Question

At what thickness will a thick convex-cancave glass lens in air
(a) serve as a telescope provided the curvature radius of its convex surface is `DeltaR = 1.5 cm` greater than that of its concave surface?
(b) have the optical equal to `-1.0 D` if the curvature radii of its convex and concave surfaces are equal to `10.0` and `7.5 cm` respectively ?

Answer 1

A telescope in normal adjustment is a zero power conbiation of lenses. Thus we require
`Phi = O = Ph_(1) + Phi_(2) - (d)/(n) Phi_(1)Phi_(2)`
But `Phi_(1) =` Power of the convex surface `= (n - 1)/(R_(0) + DeltaR)`
`Phi_(2) =` Power of the concave surface `= -(n - 1)/(R_(0))`
Thus, `O = ((n - 1) DeltaR)/(R_(0)(R_(0) + DeltaR)) + (d)/(n) ((n -1)^(2))/(R_(0)(R_(0) + DeltaR))`
So `d = (n DeltaR)/(n - 1) = 4.5 cm`. on putting the values.
(b) Here, `Phi =- 1 = (.5)/(.1) - (.5)/(.075) + (d)/(1.5) xx (.5 xx .5)/(.1 xx .075)`
`=5 - (20)/(3) + (d xx 2)/(3) xx (5 xx 20)/(3) =- (5)/(3) + (200d)/(9)`
`= (200d)/(9) = (2)/(3)` or `d =(3//100)m = 3cm`.