A concave mirror of radius 40 cm lies on a horizontla tale and wateis filled in it up t a heightof 5.00 cm. A small dust particle floats on the water surface at a point P vertically above tge pointof contact of the miror with the table. Locate the image of the dust particle as seen from a point directly above it. tEh refractie index of water is 1.33.

Explanation

The dust particle is in water.
Image by concave mirror:
`u=-5cm,f=-20cm,v=?`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(v)+(1)/(-5)=(1)/(-20)implies(1)/(v)=(1)/(5)-(1)/(20)=(3)/(20)`
`v=(20)/(3)` cm
The image of `P` is formed at `I`.
Image by refraction:
After reflection direction of incident rays is reversed `I` serves as an object.
`mu_1=(4)/(3),u=-(5+(20)/(3))=-(35)/(3)cm`
`mu_2=1,v=?`
`(mu_2)/(v)-(mu_1)/(u)=0`
`(1)/(v)-((4)/(3))/((-35)/(3))impliesv=-(35)/(4)=-8.75cm`
Fiinal image is formed at `I'.PI'=8.75cm`.