Question

In an experiment to find the focal length of a concave mirror a graph is drawn between the magnitudcs of $u$ and $v$. The graph looks like

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ is the formula which relates u \& v
$\frac{1}{u}=\frac{1}{f}-\frac{1}{v}$
Slope of the this curve can be found by differentiation $-\frac{1}{u^2}du=0+\frac{dv}{v^2}$
$\Rightarrow \frac{dv}{du}=-\frac{v^2}{u^2}$
$\frac{dv}{du}$ is the slope which is negative so either curve (c) or curve (a) is right.
Now the slope depends upon the value of u & vi.e. it keeps changing at every point as per the equation above.