A container is filled with water `(mu = 1 . 33)` upto a height of 33 . 25 cm and a concave mirror is placed 15 cm above the water level as shown in the figure. The image of an object placed at the bottom is formed 25 cm below the water level. The focal lenght of the concave mirror is approximately.

Options

A. 10 cm
B. 15 cm
C. 19 cm
D. 23 cm

Answer

C

Explanation

Given : Refractive index of water
`(mu) = 1.33`
Height of water from bottom
`(h_(1)) = 33.25`
Height of concave mirror above the water level `(h_(2))` = 15 cm and distance of image below water level `(h_(3))` = 25 cm
We know that apparent depth of object below the water level
`(h_(1)') = (h_(1))/(mu) = (33.25)/(1 . 33) = 25 cm `
Therefore distance between object and mirror when the object is placed in water
`(u) = -(h_(1)' + h_(2))`
`=-(25 + 15) = - 40 cm`
Similarly, distance between image and mirror when the object is
placed in water `(v) = - (h_(2) + (h_(3))/(mu))`
`= - (15 + (25)/(1.33))`
`= - (15 + 18 . 8) = - 33.8 cm `
We also know that relation for focal length of concave mirror (f) is
`(1)/(f) = (1)/(u) +(1)/(v) rArr (1)/(f) = (1)/(-40) +(1)/(-33.8)`
`=- 0 . 0 25 - 0 . 0 29`
= - 0 . 54