# 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 Delta

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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 ?

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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`.