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For refracrion at spherical surface, with respect to the given figure, we have   ................(1)
In eqn.(1) sign convention is not applied. v is image distance in refracting medium,  measured from point p.
R is radius of curvature which is 60 cm.

Let us analyze each case

case-(A) :-  eqn.(1) is written as  (-1/120) + (1.5/v) = (0.5/60)   or we get  v = 60 cm.

i.e image after refraction is formed at a distance 60 cm from P inside refracting medium.

Now if this image is acting as object for second refraction then we have   [ (-3/2)/60 ] + 1/v = 0.5/(-60)   or we get v = 60 cm.

Hence final image I1 is not formed on O which is 120 cm left of P , irrespective of distance d2

case-(B) :- eqn.(1) is written as (-1/240)+(1.5/v) = 0.5/60   or we get v = 120 cm

i.e image after refraction is formed at a distance 120 cm from P inside refracting medium.

Now if this image is acting as object for second refraction then we have   [ (-3/2)/120 ] + 1/v = 0.5/(-60)   or we get v = 240 cm.

Hence final image I1 is formed on O , but the distance d2 should be greater than 120,
otherwise mirror reflection will alter the location of first image and final image will not be formed at O

case-(C) and (D) are false as per the explanataion given for case -(B)
Answered by Thiyagarajan K | 05 May, 2019, 03:52: PM

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