Physics > Reflection of Light > 6.0 Motion of object and image
Reflection of Light
1.0 Introduction
2.0 Reflection of light
3.0 Basic terminologies of spherical mirrors
3.1 Paraxial approximation
3.2 Spherical mirrors
3.3 Sign convention
3.4 Ray tracing
3.5 Image formation by concave mirror
3.6 Image formation by convex mirror
4.0 Spherical mirror formulae
5.0 Magnification
6.0 Motion of object and image
6.1 Graph between $\left( {\frac{1}{v}} \right)$ and $\left( {\frac{1}{u}} \right)$
3.2 Spherical mirrors
3.3 Sign convention
3.4 Ray tracing
3.5 Image formation by concave mirror
3.6 Image formation by convex mirror
For concave mirror
The mirror formula is given by, $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
- When image formed is real and inverted
$\begin{equation} \begin{aligned} v \to - v \\ u \to - u \\ f \to - f{\text{ (concave mirror)}} \\\end{aligned} \end{equation} $
So, $$ - \frac{1}{v} - \frac{1}{u} = - \frac{1}{f}$$ or $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
Expressing the above equation as $y=mx+c$ $$\begin{equation} \begin{aligned} \frac{1}{v} = - \frac{1}{u} + \frac{1}{f} \\ m = - 1\quad or\quad \theta = 135^\circ \\ c = \frac{1}{f} \\\end{aligned} \end{equation} $$
- When image formed is virtual and erect
$\begin{equation} \begin{aligned} v \to + v \\ u \to - u \\ f \to - f{\text{ (concave mirror)}} \\\end{aligned} \end{equation} $
So, $$ + \frac{1}{v} - \frac{1}{u} = - \frac{1}{f}$$ or $$\frac{1}{v} - \frac{1}{u} = - \frac{1}{f}$$
Expressing the above equation as $y=mx+c$ $$\begin{equation} \begin{aligned} \frac{1}{v} = \frac{1}{u} - \frac{1}{f} \\ m = + 1\quad or\quad \theta = 45^\circ \\ c = - \frac{1}{f} \\\end{aligned} \end{equation} $$
The above two graph is combined in one graph as shown below,
For convex mirror
The mirror formula is given by, $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
- When image formed is real and inverted
$\begin{equation} \begin{aligned} v \to + v \\ u \to - u \\ f \to + f{\text{ (concave mirror)}} \\\end{aligned} \end{equation} $
So, $$ + \frac{1}{v} - \frac{1}{u} = + \frac{1}{f}$$ or $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
Expressing the above equation as $y=mx+c$ $$\begin{equation} \begin{aligned} \frac{1}{v} = \frac{1}{u} + \frac{1}{f} \\ m = + 1\quad or\quad \theta = 45^\circ \\ c = \frac{1}{f} \\\end{aligned} \end{equation} $$
