Frazer does Physics: 3.22 Critical angle and refractive index

June 2, 2011

Recall and use the relationship between critical angle and refractive index:

$\textup{sin}\, c = \frac{1}{n}$

c is the critical angle (in degrees,°)
n is Refractive index (no units)

Examples:

What is the refractive index of glass that has a critical angle of 42°?

$\textup{sin}\, c = \frac{1}{n}$

$\frac{1}{\textup{sin}\, c} = n$

$\frac{1}{\textup{sin}\, 42} = n$

$n = 1.494476...$

$n \approx 1.5$

What is the critical angle for diamond? (Refractive index of diamond = 2.4)

$\textup{sin}\, c = \frac{1}{n}$

$\textup{sin}^{-1} \left (\frac{1}{2.4} \right ) = c$

$c = 24.6243...$

$c \approx 25$

MattJune 6, 2011 at 4:07 PM
Excellent
First answer should be n=1.5 as you only know c to 2s.f. so answer should be to 2s.f.
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