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

index of refraction = 1.69

percentage error = 10.58%

Step-by-step 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
`(sin i)/(sin r) = n`

i = angle of incidence measured = 63.5°

r = angle of refraction measured = 32°

n = refractive index

`n = (sin 63.5^(0) )/(sin 32^(0) ) \\n = (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 =
`(1.89-1.69)/(1.89) * 100`

%error =
`(0.2)/(1.89)*100`

%error =
`(20)/(1.89)`

%error = 10.58%