Question

A concave morror of radius R is kept on a horizontal table(figure). Water $(refractiveindex=\mu )$ is poured into it upto a height h. Where should an object be placed (its distance from the water source) so that its final image is formed on itself. Consider two cases
(i) h $\to$ 0
(ii) in terms of h

Answer 1

The water -missar system behave like a planoconwex less whose curved surface is silvered , as a concave mission .

power of the peano -convex less is :

$P_l=\left|(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})\right|$ {less Makes formula}

For water, $\mu$ given , $R_1\to \infty$ and $R_2=R$

$\Rightarrow P_l=\frac{(\mu -1)}{R}$

also, power of missor in, $P_m=-\frac{2}{R}$

so, equivalent power of rivered less would be :-

$P=-(P_l+P_m)=-(\frac{M-1}{R}-\frac{2}{R})=\frac{(3-M)}{R}$

Which given focas length ,$f=-\frac{1}{p}=\frac{R}{(\mu -3)}$

and equivalent Radius of eurvature:$R=2f=\frac{2R}{\mu -3}$

so, at height $R=\frac{2R}{\mu -3},$ all rang would be normal to the silvered and where image and object wolud eoincide.

$\Rightarrow$ distance from water source ,$d=\frac{2R}{(\mu -3)}\to$ case {ii}

however , as $h\to 0,$ system behave a simple concave mirror , and placing an

object at $c$ would result forming an image at $c$ itself

$\Rightarrow d=R\to$ case {i}