Question

A concave mirror of radius R is kept on a horizontal table according the figure. Water (Refractive index = µ) is poured into it upto a hight h. Where should an object be placed so that its image is formed on it self.

• A. R above the water surface
• B. $\frac { ( \mathrm { R } - \mathrm { h } ) } { \mu }$above the water surface
• C. µR above the water surface
• D. µ(R – h) above the water surface

Answer 1

Answer: (B)

$\frac { ( \mathrm { R } - \mathrm { h } ) } { \mu }$above the water surface

Answer 2

Let x is height of an object which is placed at O position.

When, after refraction image forms at C of curvature. LM is perpendicular to concave mirror.

CA = $\frac { \mu _ { 2 } } { \mu _ { 1 } }$ OA Ž CA = $\frac { \mu } { 1 }$x ......(1)

CA = (R – h)

Putting in Ist equation

(R – h) = µx

distance of object from surface of water

x = $\frac { ( \mathrm { R } - \mathrm { h } ) } { \mu }$

option B is correct