Question Part
Points
Submissions Used
1 2 3 4
0/0.37 0/0.37 –/0.37 –/0.37
4/15 1/15 0/15 0/15
Total
0/1.48
...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° .
(a) What are the indices of refraction for red and blue light in diamond?
(b) What is the ratio of the speed of red light to the speed of blue light in diamond?
To find the answers to these questions, we need to use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the media involved. The equation is given by:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the indices of refraction of the initial and final media, θ1 is the angle of incidence, and θ2 is the angle of refraction.
(a) To find the indices of refraction for red and blue light in diamond, we can use Snell's law with the given angles of incidence and refraction. Let's start with the red light:
n_air * sin(θ_air) = n_diamond * sin(θ_red)
We know that n_air is approximately equal to 1 since it is air, and θ_air is given as the angle of incidence, 46.05°. The value of sin(θ_air) can be found using a scientific calculator or a trigonometric table.
Next, we can rearrange the equation to solve for n_diamond:
n_diamond = (n_air * sin(θ_air)) / sin(θ_red)
Substituting the given values, we have:
n_diamond = (1 * sin(46.05°)) / sin(17.38°)
Calculating this using trigonometric functions, we find the value of n_diamond for red light.
We can repeat the same process to find n_diamond for blue light using the given angles of refraction. The equation will be:
n_air * sin(θ_air) = n_diamond * sin(θ_blue)
Solving for n_diamond again using the given values will give us the index of refraction for blue light in diamond.
(b) The speed of light in a medium is inversely proportional to its index of refraction. The ratio of the speed of red light to the speed of blue light in diamond can be found using the indices of refraction.
The speed of light in a vacuum is constant, so we can write the following equation:
v_red / v_blue = n_blue / n_red
where v_red and v_blue are the speeds of red and blue light in diamond, and n_red and n_blue are their corresponding indices of refraction determined in part (a).
Substituting the values, we can find the ratio of the speeds of red and blue light in diamond.
By following these steps, we can find the answers to both (a) and (b).