Water (with refractive index = 4 3 ) in a tank is 18 ~cm deep. Oil of refractive index 7 4 lies on water making a convex surface of radius of curvature R=6 ~cm as shown. Consider oil to act as a thin lens. An object S is placed 24 ~cm above water surface. The location of its image is at x ~cm above the bottom of the tank. Then, x is

Step-by-step solution

Two refractions will take place, first from spherical surface and the other from the plane surface. So, applying ₂ v - ₁ u = ₂- ₁ R two times with proper sign convention. Ray of light is travelling downwards. Therefore, downward direction is taken as positive direction. gathered 7 / 4 v - 1.0 -24 = 7 / 4-1.0 +6 4 / 3 (18-x) - 7 / 4 v = 4 / 3-7 / 4 gathered Solving these equations, we get x=2 ~cm Answer is 2 . Analysis of Question (i) Question is moderately difficult from calculation point of view, otherwise it is s