A beaker is filled with water as shown in figure (a). The bottom surface of the beaker is a concave mirror of large radius of curvature and small aperture. The height of water is `h = 40 cm`. It is found that when an object is placed 4 cm above the water surface, the image coincides with the object. Now the water level h is reduced to zero but there will still be some water left in the concave part of the mirror as shown in figure (b). The new height of the object h' above the new water surface so that the image again coincides with the object, will be (Refractive index of water `= 4//3`)

Options

A. 34 cm
B. 10 cm
C. 74 cm
D. zero

Answer

A

Explanation

The image shall coincide with object O if the ray starting from O is incident normally on mirror (figure 1)
`:. X = 4 xx(4)/(3) = (16)/(3)`
In second case the image shall coincides with object O it ray starting from O is incident normally on mirror (figure 2)

`(136)/(3)=hxx(4)/(3) or h=(136)/(3)xx(3)/(4) =34 cm`