Question

A linear object of height $10cm$ is kept in front of a concave mirror of radius of curvature $15cm$, at a distance of $10cm$. The image formed is

• A. Magnified and erect
• B. Magnified and inverted
• C. Diminished and erect
• D. Diminished and inverted

Answer 1

Answer: (B)

Magnified and inverted

Object distance $u=-10$ cm

Radius of curvature of concave mirror $R=-15$ cm

Thus its focal length $f=\frac{R}{2}=-\frac{15}{2}$ cm

Using mirror formula : $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\therefore$ $\frac{1}{v}+\frac{1}{-10}=-\frac{2}{15}$

$⟹$ $v=-30$ cm

Magnification $m=\frac{-v}{u}$

$\therefore$ $m=\frac{-(-30)}{-10}=-3$

Negative sign indicates that the image formed is inverted in nature.

Magnitude of magnification is greater than $1$ which indicates that magnified image is formed.