An object of size 7.5 cm is placed in front | vedclass

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(B) Given: Object size $O = 7.5 \ cm$,Radius of curvature $R = 25 \ cm$,Object distance $u = -40 \ cm$.For a convex mirror,the focal length $f = R/2 =

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$1.78$

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(B) Given: Object size $O = 7.5 \ cm$,Radius of curvature $R = 25 \ cm$,Object distance $u = -40 \ cm$.For a convex mirror,the focal length $f = R/2 = 25/2 = 12.5 \ cm$.Using the magnification formula for a mirror: $m = \frac{I}{O} = -\frac{v}{u}$.Also,from the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,we have $v = \frac{uf}{f - u}$.Substituting $v$ into the magnification formula: $\frac{I}{O} = -\left(\frac{uf}{f - u}ight) \cdot \frac{1}{u} = \frac{f}{f - u}$.Substituting the values: $\frac{I}{7.5} = \frac{12.5}{12.5 - (-40)} = \frac{12.5}{52.5}$.$I = 7.5 	imes \frac{12.5}{52.5} = 7.5 	imes \frac{1}{4.2} \approx 1.78 \ cm$.

An object of size $7.5 \ cm$ is placed in front of a convex mirror of radius of curvature $25 \ cm$ at a distance of $40 \ cm$. The size of the image should be ........ $cm$.

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