Question

who can solve this problem give me answer

Answer 1

Use the following:


$\frac{R}{2} = f \\ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ m = - \frac{v}{u} = \frac{I}{O}$
Here, R is the radius of Curvature, f is the focal length of the mirror, v is the image distance, u is the object distance, I is size of the Image, O is size of the object and m is the magnification.


Since Convex mirror produces only virtual images, the magnification
$- \frac{v}{u} = \frac{1}{2} \\ - 2v = u$
Use this in the mirror formula,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ \frac{1}{v} - \frac{1}{2v} = \frac{2}{R } \\ \frac{1}{2v} = \frac{2}{R} \\ v = \frac{R}{4} \\ v = \frac{40}{4} \\ v = 10cm$
So the image distance is 10cm behind the mirror.