91Ó°ÊÓ

The object distance,$p=+17\mathrm{cm}$

The focal length of the spherical mirror,$f=-14\mathrm{cm}$

The mirror is convex mirror.

Use equations of the radius of curvature and lateral magnification for a spherical mirror. Also, need to use equation 34.4 to calculate the distance of the image. Using these values, determine the nature of the image.If the image distance is negative, then the image is virtual and as the magnification ratio is positive, the image is upright.

Formulae:

The radius of curvature is related to the focal length of the mirror by the flowing formula.

$r=2f$

The spherical mirror equation is,

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

The magnification equation is as below.

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

Where, $m$is the magnification, $p$is the pole,$f$ is the focal length.

Use the following formula to find the radius of curvature.

$r=2×f$

Since the mirror is convex, the focal length must be negative, i.e., .$f=-14\mathrm{cm}$

$\begin{array}{c}r=-2×14\mathrm{cm}\\ =-28\mathrm{cm}\end{array}$

Hence, the radius of curvature is $-28\mathrm{cm}$.

Write the spherical mirror equation as below.

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

Rearranging it for the image distance.

$i=\frac{pf}{\left(p-f\right)}$

Substitute known values in the above equation.

$\begin{array}{c}i=\frac{17\mathrm{cm}×\left(-14\mathrm{cm}\right)}{\left(17-\left(-14\right)\right)\mathrm{cm}}\\ =-7.7\mathrm{cm}\end{array}$

Hence, the image distance is $-7.7\mathrm{cm}$.

The magnification ratio is define as,

$\begin{array}{c}M=\frac{-i}{p}\\ =\frac{7.7\mathrm{cm}}{17\mathrm{cm}}\\ =+0.45\end{array}$

Hence, the magnification ratio is $0.45$.

Since the image distance is negative. Therefore, the image is virtual.

As magnification is positive. Thus, the image is non-inverted.

A virtual image is formed on the opposite side of the mirror from the object. Hence, the image is opposite side of the mirror.