Question

An object height 7.5 cm is placed in front of a convex mirror of radius of curvature 25 cm at a distance of 40 cm. The height of the image should be

• A. $3.41cm$
• B. $1.78cm$
• C. $1cm$
• D. $0.8cm$

Answer 1

The correct option is B $1.78cm$

Size of the object $\left(h_0\right)=7.5cm$

Radius of curvature $\left(R\right)=25cm$

Object distance $\left(u\right)=-40cm$

Focal length $f=\frac{R}{2}=\frac{25}{2}=12.5cm$

Size of the image $\left(h_i\right)=?$

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

$\Rightarrow \frac{1}{12.5}=-\frac{1}{40}+\frac{1}{v}$

$\Rightarrow v=\frac{40\times 12.5}{40+12.5}=9.52cm$

$\underset{–}{\text{Magnification:}}$

$\begin{array}{cc}& -\frac{v}{4}=\frac{hi}{ho}\\ \Rightarrow & -\frac{9.52}{-40}=\frac{4i}{7.5}\\ \to & h_i=1.785cm\end{array}$

$\therefore \left(B\right)$ is the correct option.