An observer looks directly down at a mark at the bottom of a container filled with a transparent liquid. The actual depth of the liquid is 24 cm . If the time taken for light to travel from the mark to the liquid surface is 1.2 ns , the apparent depth of the mark as seen by the observer is: (Given the speed of light in vacuum is 3 10^8 m/s )

Step-by-step solution

The actual depth of the liquid is d = 24 cm = 0.24 m . The time taken for light to travel this distance in the liquid is t = 1.2 ns = 1.2 10⁻⁹ s . The speed of light in the liquid is: v = d t = 0.24 1.2 10⁻⁹ = 2 10^8 m/s The refractive index of the liquid is: = c v = 3 10^8 2 10^8 = 1.5 The apparent depth d' of the mark is given by: d' = d = 24 cm 1.5 = 16 cm Answer: 16 cm