A concave mirror of focal length 30 cm is placed on the flat horizontal surface with its concave side up. Water with refractive index 1.33 is poured into the lens. Where should an object be placed if its image is to be captured on a screen with a magnification of 2?

Explanation

`y=mux=(4)/(3)x`
For the mirror, `u=-y=(4)/(3)x`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)-(3)/(4x)=(1)/(-30)`
`v=((60x)/(2x-45))`
Let the final image is formed at a distance z from the mirror, then
`((60x)/(2x-45))(1)/(z)=mu=(4)/(3)` and `(z)/(x)=2` (magnification)
Solving, we get `x=33.75 cm`