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Q.
An object is placed in front of a convex mirror of radius of curvature $20 cm$. Its image is formed $8 cm$ behind the mirror. The object distance is
Ray Optics and Optical Instruments
Solution:
According to new cartesian sign convention Object distance, $u=$ ?
Image distance, $v=8 \,cm$
Focal length of a convex mirror, $f=\frac{R}{2}=10 \,cm$
According to the mirror formula, $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$ Substituting the values, we get
$\frac{1}{u}+\frac{1}{8}=\frac{1}{10}$
$ \Rightarrow \frac{1}{u}=\frac{1}{10}-\frac{1}{8}$
or $u=-40 \,cm$
Negative sign shows that the object is placed in front of the convex mirror.