1.

A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is approximately :

Answer»

`bsqrt((U-f)/(f))`
`bsqrt((f)/(u-f))`
`b((u-f)/(f))`
`b((f)/(u-f))^(2)`

Solution :(d) For a mirror `(1)/(v) + (1)/(u) = (1)/(f)`
Differentiating we get `- ((1)/(v^(2)) (dv)/(DU) - (1)/(u^(2)) = 0`
`therefore(dv)/(du)=(v^(2))/(u^(2))=-((v)/(u))^(2)thereforem=-((v)/(u))^(2) "" ...(i)`
Further `(1)/(v) + (1)/(u) = (1)/(f)`
`(u)/(v)+1=(u)/(f)therefore(v)/(u)=(f)/(u-f) "" ...(ii)`
As `m=(I)/(O)=(I)/(b) ""...(iii)`
From (i) and (iii),
`(I)/(b)=-((v)/(u))^(2)=-((f)/(u-f))^(2), "from eqn," (ii)`
`therefore(I)/(b)=-((f)/(u-f))^(2)`
`therefore I=b((f)/(u-f))^(2)` (numerically).


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