Sunlight strikes a piece of crown glass at an angle of incidence of 35.8 degrees. Calculate the difference in the angle of refraction between a red (660. nm) and a green (550. nm) ray within the glass. The indices of refraction for the red and the green are n = 1.520 and n = 1.526, respectively.
Use Snell's law to compute the angle of refraction for each color. Call the angles A1 and A2. Then compute the difference, A1 - A2. .
Red:
sin35.8 = 1.520*sinA1
sinA1 = 0.38484
A1 = 22.63 degrees
Green:
sin35.8 = 1.526*sinA2.
A2 = ___
A1 - A2 = ___
Thanks
To calculate the difference in the angle of refraction between the red and green rays, we first need to calculate the angle of refraction for each ray separately using Snell's Law.
Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media. Mathematically, it can be written as:
n1 * sin(θ1) = n2 * sin(θ2)
Where:
n1 and n2 are the refractive indices of the two media (in this case, crown glass)
θ1 is the angle of incidence
θ2 is the angle of refraction
First, let's calculate the angle of refraction for the red ray with a wavelength of 660 nm and a refractive index of n = 1.520.
1. Convert the angle of incidence to radians:
θ1 = 35.8 degrees = 35.8 * π / 180 radians
2. Apply Snell's Law:
1.520 * sin(θ1) = n2 * sin(θ2)
sin(θ2) = 1.520 * sin(35.8 * π / 180)
θ2 (red) = arcsin(1.520 * sin(35.8 * π / 180))
Next, let's calculate the angle of refraction for the green ray with a wavelength of 550 nm and a refractive index of n = 1.526.
1. Convert the angle of incidence to radians:
θ1 = 35.8 degrees = 35.8 * π / 180 radians
2. Apply Snell's Law:
1.526 * sin(θ1) = n2 * sin(θ2)
sin(θ2) = 1.526 * sin(35.8 * π / 180)
θ2 (green) = arcsin(1.526 * sin(35.8 * π / 180))
Finally, calculate the difference in the angle of refraction between the red and green rays:
Difference = θ2 (green) - θ2 (red)