Final answer:
Using Snell's law, the index of refraction for the diamond is calculated as approximately 2.404, when light enters the diamond from air with an incidence angle of 30° and a refraction angle of 12°.
Step-by-step explanation:
To determine the index of refraction for the diamond when a beam of light enters from air at an angle of 30° from the normal and the angle of refraction is 12°, we can use Snell's law. This law relates the angles of incidence and refraction to the indices of refraction for the two media through which the light is traveling:
n1 * sin(θ1) = n2 * sin(θ2)
Here, n1 is the index of refraction of air which is 1.00, θ1 (theta1) is the angle of incidence which is 30°, n2 is the index of refraction of diamond which we wish to find, and θ2 (theta2) is the angle of refraction which is 12°. Plugging in the values we have, we can rearrange the formula to solve for n2:
n2 = n1 * sin(θ1) / sin(θ2)
Substitute the known values:
n2 = 1.00 * sin(30°) / sin(12°)
n2 = 1.00 * 0.5 / 0.2079
n2 = 2.404
Therefore, the index of refraction for the diamond is approximately 2.404.