Interactive Solution 26.7 offers one model for problems like this one. In a certain time, light travels 3.97 km in a vacuum. During the same time, light travels only 2.61 km in a liquid. What is the refractive index of the liquid

Refractive Index = 1.52

Explanation:

As we know speed of light in vaccum is 3 x 10^8 meters per second and distance tavelled by light is 3.97 km or 397000m.

Time taken by light in vaccum = distance / speed = 397000 / 3 x 10^8 = 1.323 x 10^-3 s

Speed of light in liquid = distance / time taken = 261000 / 1.323 x 10^-3 = 197278911 ms^-1 = 1.972 x 10^ 8 ms^-1

According to Snell's law

Refractive index = speed of light in vaccum / speed of light in medium = 3 x 10^8 ms^-1 / 1.972 x 10^8 ms^-1 = 1.52