light moves from olivine (n= 1.670) into onyx. If the critical angle for olivine is 62.85 degrees , what is the index of refraction for onyx ?
1.5
To find the index of refraction for the onyx, we can use Snell's law, which relates the angles and indices of refraction of light passing through two different mediums. The formula is as follows:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the index of refraction of the first medium (olivine in this case)
- theta1 is the angle of incidence (in this case, the critical angle for olivine)
- n2 is the index of refraction of the second medium (onyx in this case)
- theta2 is the angle of refraction (which we need to find)
Rearranging the formula, we can solve for n2:
n2 = (n1 * sin(theta1)) / sin(theta2)
Substituting in the given values:
n1 = 1.670 (olivine)
theta1 = 62.85 degrees (critical angle for olivine)
To find theta2, we can use the relationship between the critical angle and the angle of refraction:
theta2 = 90° - theta1
Substituting the values:
theta2 = 90° - 62.85°
Now, we can substitute all the known values into the formula:
n2 = (1.670 * sin(62.85°)) / sin(90° - 62.85°)
Calculating this expression will give us the index of refraction for onyx.