A diamond in air is illuminated with white light. On one particular facet, the angle of incidence is 46.05°. Inside the diamond, red light (ë = 660.00 nm in vacuum) is refracted at 17.38° with respect to the normal; blue light (ë = 470.00 nm in vacuum) is refracted at 17.09°
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To understand the refraction of light in a diamond, we need to apply the laws of refraction and Snell's law. Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two media. Mathematically, Snell's law can be expressed as:
n1 sin(θ1) = n2 sin(θ2)
Where:
n1 is the refractive index of the first medium (in this case, air)
n2 is the refractive index of the second medium (in this case, diamond)
θ1 is the angle of incidence
θ2 is the angle of refraction
To find the refractive index of diamond for red light and blue light, we can rearrange Snell's law as follows:
n2 = (n1 sin(θ1)) / sin(θ2)
First, let's calculate the refractive index of diamond for red light:
θ1 = angle of incidence = 46.05°
θ2 = angle of refraction for red light = 17.38°
n1 = refractive index of air = 1 (since light is incident from air)
n2 for red light = (1 * sin(46.05°)) / sin(17.38°)
Using a scientific calculator, we can find that n2 for red light is approximately 2.408.
Now, let's calculate the refractive index of diamond for blue light:
θ1 = angle of incidence = 46.05°
θ2 = angle of refraction for blue light = 17.09°
n1 = refractive index of air = 1 (since light is incident from air)
n2 for blue light = (1 * sin(46.05°)) / sin(17.09°)
Again, using a scientific calculator, we can find that n2 for blue light is approximately 2.419.
Therefore, the refractive index of diamond for red light is approximately 2.408, and for blue light, it is approximately 2.419.