Question

A flat sheet of ice has a thickness of 2.20 cm. It is on top of a flat sheet of crystalline quartz that has a thickness of 1.50 cm. Light strikes the ice perpendicularly and travels through it, and then through the quartz. In the time it takes the light to travel through the two sheets, how far would it have traveled in a vacuum?

Answer 1

Answer:

$Distance_{vaccum}=5.19cm$

Explanation:

The speed of light in these mediums shall be lower than that in vacuum thus the total time light needs to cross both the media are calculated as under

Total time = Time taken through ice + Time taken through quartz

Time taken through ice = Thickness of ice / (speed of light in ice)

$T_{ice}=\frac{2.20\times 10^{-2} \times \mu _{ice}}{V_{vaccum}}$

$T_{quartz}=\frac{1.50\times 10^{-2} \times \mu _{quartz}}{V_{vaccum}}$

Thus in the same time the it would had covered a distance of

$Distance_{vaccum}=Totaltime\times V_{vaccum}\\\\Distance_{vaccum}=10^{-2}[2.20\mu _{ice+1.50\mu _{quartz}}]$

we have

$\mu _{ice}=1.309\\\\\mu _{quartz}=1.542$

Applying values we have

$Distance_{vaccum}=10^{-2}[2.20\times 1.309+1.50\times 1.542]$

$Distance_{vaccum}=5.19cm$