You shine a laser on a plastic prism made from an unknown material and measure the...

You shine a laser on a plastic prism made from an unknown material and measure the angles relative to the normal that the light takes both inside and outside the medium. You make a plot of sin ?_inside versus sin ?_outside for the plastic object and calculate the slope of best-fit line of your plot to be 0.79365 ± 0.05669. What is the index of refraction of the plastic object?

Correct Answer: 1.26 +/- 0.09

How do you get the 0.09 uncertainty?

Expert Solution

Using Snell's law,
n1 sino = n2 sini
Where n1 is the refractive index of air, n1 = 1 and n2 is the refractive index of the material
sini/sino = 1/n2 = 0.079365 0.05669
n2 = 1/(0.079365 0.05669)
= 1/[0.079365 x (1 0.714295)]
= 1.26 x (1 0.714295)^-1.
Expanding the second term in the bracket binomially,
n2 = 1.26 [1 0.714295 (0.714295)² (0.714295)³ ...]
We can neglect all the higher powers
n2 = 1.26[(1 0.714295)]
= 1.26 0.09

genius_generous answered 2 years ago

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