Question

A $2.0cm$ tall object is placed $15cm$ in front of a concave mirror of focal length $10cm$. What is the size and nature of the image?

• A. $4cm$, real
• B. $4cm$, virtual
• C. $1.0cm$, real
• D. None of these

Answer 1

The correct option is A $4cm$, real

According to new cartesian sign convention,
Object distance, $u=-15cm$
Focal length of the concave mirror, $f=-10cm$
Height of the object, $h_0=2cm$
According to mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{-10}-\frac{1}{1-5}=\frac{1}{-10}+\frac{1}{15}$
or $v=-30cm$
The image is formed at a distance of $30cm$ from the mirror on the same side of the object.
It is a real image.
Magnification of the mirror, $m=\frac{-v}{u}=\frac{h_1}{h_0}$
$\Rightarrow \frac{-(-30)}{-15}=\frac{h_1}{2}\Rightarrow h_I=-4cm$.
Negative sign shows that image is inverted.
The image is real, inverted, of size $4cm$ at a distance of $30cm$ in front of the mirror.