Question

An object is placed in front of a convex mirror of radius of curvature $20cm$. Its image is formed $8cm$ behind the mirror. The object distance is

• A. 20 cm
• B. 40 cm
• C. 60 cm
• D. 80 cm

Answer 1

Answer: (B)

According to new cartesian sign convention Object distance, $u=$ ?
Image distance, $v=8cm$
Focal length of a convex mirror, $f=\frac{R}{2}=10cm$
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 $u=-40cm$
Negative sign shows that the object is placed in front of the convex mirror.