91Ó°ÊÓ

The magnification, $m=-0.50$.

The object’s distance, $p=+60cm$.

The properties of mirror can be used to find the type of mirror. Magnification and object distance can be used to find image distance and focal length, and from focal length, radius of curvature can be found. And from image distance, it is identify whether image is inverted or not.

Formulae:

The radius of curvature is,

$r=\text{2}f$

The spherical mirror equation is,

$\frac{\text{1}}{f}=\frac{\text{1}}{i}+\frac{\text{1}}{p}$

The magnification is,

$m=\frac{-i}{p}$

Here, $r$is the radius of curvature, $f$is the focal length, $p$is the object distance from mirror, and $i$is the image distance.

As magnification ratio is less than zero and negative, it means image is smaller than object. Hence, mirror is concave type.

Use following formula to find focal length as,

$\begin{array}{rcl}m& =& \frac{-i}{p}\\ i& =& -mp\end{array}$

$\begin{array}{rcl}i& =& -\left(-0.5\right)×\left(+60\right)\\ & =& +30cm\end{array}$,

Now focal length is as follows,

$\frac{\text{1}}{f}=\frac{\text{1}}{i}+\frac{\text{1}}{p}$,

$\begin{array}{rcl}\frac{\text{1}}{f}& =& \frac{\text{1}}{+30\text{cm}}+\frac{\text{1}}{+60\text{cm}}\\ & =& 0.033{\text{cm}}^{-1}+0.0167{\text{cm}}^{-1}\\ & =& 0.0497{\text{cm}}^{-1}\end{array}$

$\begin{array}{rcl}f& =& \frac{1}{0.0497{\text{cm}}^{-1}}\\ & =& 20.12\text{cm}\\ & ≈& \text{20 cm}\end{array}$

Hence, the focal length is 20 cm.

Use the following formula to find the radius of curvature,

$\begin{array}{rcl}r& =& 2×f\\ & =& 2×20\text{cm}\\ & =& 40\text{cm}\end{array}$

Hence, the radius of curvature of the spherical mirror is 40 cm.

Object distance is$p=+60cm$ as given in table.

According to part (b) the image distance is $i=+30cm$.

Magnification ratio is $m$is $-0.50$as given in the table.

Since image distance is positive, image is real.

As magnification is negative so image is inverted.

An image is formed on same side of mirror from the object.