A spherical mirror is placed 10 cm below the level of water. A point object is placed in air 30 cm above the water surface on the axis of the mirror such that two images seen by an observer above the water surface coincide. The images are formed by partial reflection at the water surface and due to emerging light after reflection from the mirror. Find the focal length of the mirror. ( μ water = 4 3 )

Step-by-step solution

For partial reflection, the final image should be 30 cm below water surface i.e. 20 cm below the mirror. For the image 30 cm below surface, its actual depth should be h = 3 0 4 3 = 4 0 cm below surface i.e. 30 cm below the mirror For mirror, u = - 1 0 + 3 0 4 3 ⇒ u = - 50 cm and v = 30 cm 1 f = - 1 50 + 1 30 = - 3 + 5 10 = 2 150 or f = 75 cm convex mirror of focal length 75 cm . (diagram drawn was just for reference actually it should be a convex mirror but it was not known so we assumed concave but at final calcul