Answer :
The magnitude of smaller and larger radius is 45mm and 90mm respectively.
Using lens makers formula:
1/f = (n-1) (1/ [tex]r_{1}[/tex] - 1/ [tex]r_{2}[/tex])
where n is the index of refraction, [tex]r_{1}[/tex] and f is the focal length and the curvature's radius of the first surface the light touches, and [tex]r_{2}[/tex] is the second's radius of curvature. The radius of one surface is two times that of the other, such that one is concave to the incoming light and the other is convex.
Plugging in the values we get:
1/f = (n-1) (1/ [tex]r_{1}[/tex] + 1/ [tex]2r_{1}[/tex]) = 3(n-1) / 2[tex]r_{1[/tex]
(a) For magnitude of smaller radius:
3(n-1)f / 2 = 3(1.5-1)(60) / 2 = 45mm
(b) For larger radius:
[tex]r_{2} = 2r_{1}[/tex] = 90mm
Therefore, the magnitude of smaller and larger radius is 45mm and 90mm respectively.
Learn more about radius of curvature here:
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