Answer:
t = 2.13 10-10 s
, d = 6.39 cm
Explanation:
For this exercise we use the definition of refractive index
n = c / v
Where n is the refraction index, c the speed of light and v the speed in the material medium.
The refractive indices of ice and crown glass are 1.13 and 1.52, respectively, therefore the speed of the beam in the material medium is
v = c / n
As the beam strikes perpendicularly, the beam path is equal to the distance of the leaves, there is no refraction, so we can use the uniform motion relationships
v = d / t
t = d / v
t = d n / c
Let's look for the times on each sheet
Ice
t₁ = 1.4 10⁻² 1.31 / 3 10⁸
t₁ = 0.6113 10⁻¹⁰ s
Crown glass (BK7)
t₂ = 3.0 10⁻² 1.52 / 3.0 10⁸
t₂ = 1.52 10⁻¹⁰ s
Time is a scalar therefore it is additive
t = t₁ + t₂
t = (0.6113 + 1.52) 10⁻¹⁰
t = 2.13 10-10 s
The distance traveled by this time in a vacuum would be
d = c t
d = 3 10⁸ 2.13 10⁻¹⁰
d = 6.39 10⁻² m
d = 6.39 cm
