A concave mirror of radius of curvature one meter is placed at the bottom of a tank of water. The mirror forms an image of the sun when it is directly overhead. Calculate the distance of the images from the mirror for (a) `80cm` and (b) `40cm` of water in the tank ( `mu=4//3` for water)

Explanation

(a)

Focal length of mirror `f=R/2=(100)/(2)=50cm`
For parallel rays, image is formed at focus of mirror.
`PI=50cm`
(b) When depth of water is `40cm`

`musini=1xxsinr`
As angles i and r are small, `sin i =tan i`, `sin r=tanr`
`mutani=tanr`
`4/3*(AB)/(OB)=(AB)/(BI)`
`4/3*(1)/(10)=(1)/(BI)`
`BI=7.5cm`
`PI=40+BI=40+7.5=47.5cm`
Alternatively:
`mu(BI)=BO`
`4/3xxBI=10`
`BI=7.5cm`