Explanation:
Given that,
Object distance, u = -50 cm
Radius of curvature of the convex mirror, R = 40 cm
Focal length of the convex mirror, [tex]f=\dfrac{R}{2}=20\ cm[/tex]
We need to find the magnification of the mirror. Firstly, it is required to find the image distance using formula as:
[tex]\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}[/tex]
[tex]\dfrac{1}{f}-\dfrac{1}{u}=\dfrac{1}{v}[/tex]
[tex]\dfrac{1}{20}-\dfrac{1}{-50}=\dfrac{1}{v}[/tex]
v = 14.28 cm
Magnification of the mirror,
[tex]m=\dfrac{-v}{u}[/tex]
[tex]m=\dfrac{-14.28}{-50}[/tex]
m = 0.28
So, the magnification of the mirror is 0.28.Hence, this is the required solution.
