Light is refracted as it travels from a point A in medium 1

Light is refracted as it travels from a point A in medium 1 to a point B in medium 2. If the index of refraction is 1.33 in medium 1 and 1.51 in medium 2, how long does it take light to go from A to B, assuming it travels 311 cm in medium 1 and 151 cm in medium 2?

t(Total) = _______

Solution

ndex of refraction in medium 1 n1 = 1.33

index of refraction in medium 2 n2 = 1.51

distance travels in medium 1   s1 = 311 cm = 3.11 m

distance travels in medium 2    s2 = 151 cm = 1.51 m

we know that

The index of refraction is the ratio of the speed of light in vacuum relative to that in the considered medium . so

velocity of light in medium 1   v1 = c/n1 = 3*10^(8) / 1.33 = 2.25*10^8 m/s

velocity of light in medium 2 v2 = c/n2 = 3*10^8 / 1.51 = 1.98*10^8 m/s

t1 = s1/v1 = 3.11 / 2.25*10^8 = 1.388*10^(-8) s = 13.88 nanosecond

t2 = s2 / v2 = 1.51 / 1.98*10^8 = 0.961*10^(-8) s = 7.62 nanosecond

total time to go from medium A to B = 13.88 + 7.62 = 21.5 nanosecond