Q25 of 27 Page 132

The distance between two point sources of light is 24cm .Where should a convergent lens with a focal length of f = 9cm be placed between them to obtain the images of both sources at the same Point? (AS7)

Let the first point source be located at the distance u1 & its image is formed at the distance v1. Similarly, the second point source be located at the distance u2 & its image located at v2.

Given: focal length f = 9 cm


Distance between two sources = 24 cm


For first point source:



As both the images are at the same point therefore v1 = v2 = v


..(1)


For second point source:



…(2)


[u1 + u2 = 24 cm]


Adding (1) & (2)





24 u1 – u12 = 108


U12-24u1 + 108 = 0


U12 - 18u1 - 6u1 + 108 = 0


(u1-6)(u1-18) = 0


u1 = 6 cm or u1 = 18 cm


So the lens is kept at the distance of 6 cm or 18 cm from the first point source.


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