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`.