What is the angle of refraction (relative to the boundary

What is the angle of refraction (relative to the boundary normal) of a diamond in contact with water according to Snell's law? The indices of refraction for water and diamond are respectively 1.33 and 2.42.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Freddy Doyle
The equation for this situation is
${n}_{water}\mathrm{sin}{\theta }_{water}={n}_{diamond}\mathrm{sin}{\theta }_{diamond}$
Since we know ${\theta }_{water}$ , and ${n}_{water}\approx 1.33$ and ${n}_{diamond}\approx 2.42$, solve for ${\theta }_{diamond}$.
${\theta }_{diamond}=\mathrm{arcsin}\left(\frac{{n}_{water}}{{n}_{diamond}}\mathrm{sin}{\theta }_{water}\right)$
Remember that angles of refraction are with respect to the normal.

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee