Question

The index of refraction of a clear plastic is listed as 1.89 in the book, but you measured the angle of incidence 63.5° and the angle of refraction 32°. What index of refraction did you calculate and what is the percentage error?

Answer 1

Answer:

index of refraction = 1.69

percentage error = 10.58%

Explanation:

According to Snell's law, the ratio of the sine of angle of incidence to the sine of angle of refraction is a constant for a given pair of media. The constant is known as the refractive index.

Mathematically $\frac{sin i}{sin r} = n$

i = angle of incidence measured = 63.5°

r = angle of refraction measured = 32°

n = refractive index

$n = \frac{sin 63.5^{0} }{sin 32^{0} } \\n = \frac{0.8949}{0.5299}\\ n = 1.69$

The index fraction calculated is approx. 1.69.

If the index of refraction of a clear plastic as listed in the book is 1.89 and the calculated is 1.69, the percentage error will be calculated as thus;

%error = $\frac{1.89-1.69}{1.89} * 100$

%error = $\frac{0.2}{1.89}*100$

%error  = $\frac{20}{1.89}$

%error  = 10.58%