Question

A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let O be the pole of the mirror and C be its center of curvature. A point object is placed at C, whose real image is also formed at C. If the mirror is now filled with water, the image will be

• A. real and will remain at C
• B. real, and will be located above C
• C. virtual, and will be located below O
• D. real,and will be located between C and O

Answer 1

The correct option is D real,and will be located between C and O

consider the arrangement to be combination of plano convex lens and a concave mirror

let $R$ be radius of curvature

$f_{lens}=\frac{R}{2}$ and $f_{mirror}=\frac{R}{2}$

first image is formed by lens

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{R}=\frac{2}{R}$

$v=R$

now this serves as virtual image for mirror

$u=+R$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{R}=\frac{-2}{R}$

$v=\frac{-R}{3}$

this again serves as virtual image for the lens

$u=\frac{R}{3}$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{3}{R}=\frac{2}{R}$

$v=\frac{R}{5}$

hence the image is real and formed between O and C

option $D$ is correct