1.

When an object is placed at a distance of `60 cm` from a convex spherical mirror, the magnification produced is `1//2`. Where should the object be placed to get a magnification of `1//3` ?

Answer» Here, `u_(1) = -60 cm, m_(1) = (1)/(2)`
`u_(2) = ?, m_(2) = (1)/(3)`
As `m_(1) = -(v_(1))/(u_(1)) :. (1)/(2) = -(v_(1))/(-(-60)), v_(1) = 30 cm`
From `(1)/(f) = (1)/(v_(1)) + (1)/(u_(1)) = (1)/(30) - (1)/(60) = (1)/(60)`
`f = 60 cm`
Again, `m_(2) = -(v_(2))/(u_(2)) = (1)/(3), v_(2) = -(u_(2))/(3)`
From `(1)/(v_(2)) + (1)/(u_(2)) = (1)/(f)`
`(1)/(u_(2)) = (1)/(f) - (1)/(v_(2)) = (1)/(60) + (3)/(u_(2))`
or `(1)/(u_(2)) - (3)/(u_(2)) = (1)/(60), u_(2) = -120 cm`


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