An equiconvex lens having μ = 1.5 and radius of curvature 10 cm is cut into four equal parts as shown in the diagram. Two parts are used to form the image as shown in the diagram. Taking O as origin (

Question

An equiconvex lens having μ = 1.5 and radius of curvature 10 cm is cut into four equal parts as shown in the diagram. Two parts are used to form the image as shown in the diagram. Taking O as origin ( 0 , 0 ) , if the x and y coordinates of the image are ( n cm , m cm ) , then the value of m n ​ is:

TestHub · Accepted Answer

The cross-cut makes each quarter plano-convex, so:
$f = \frac{R}{μ - 1} = \frac{10}{0.5} = 20$ cm
Lens 1 (axis on the given axis) has the object at its focal length and collimates the beam:
$u = 20$ cm $= f$
Lens 2 (axis 2 mm higher) focuses this parallel beam at its focal point, 20 cm beyond, on its own axis.
$n = 40$ cm
$m = 0.2$ cm
$\frac{n}{m} = 200$ = printed key
(Printed closing line "so nm = 8" is a typo.)

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