The refractive index of a medium changes with the wavelength of incident light. Typically, the shorter the wavelength the larger the refractive index.
Fused quartz has a refractive index of 1.47 for indigo light of 400 nm in wavelength, and a refractive index of 1.46 for green light of 550 nm in wavelength.
If rays of indigo and green light enter fused quartz from air, making an angle of 45º, the angle that separates two rays as they travel through the fused quartz is closest to ...
43.2º
42.9º
29.0º
28.8º
0.37º
0.22º
Test on monday. Help please
Both rays bend by nearly the same amount, so the answer will be one of the smaller numbers.
The angle of refraction (measured from the normal to the surface) is given by
sin Ar = sin Ai/N, where Ai is the angle if incidence (45 degrees in this case)
For the indigo ray,
sin Ar = 0.4810 Ar = 28.75 degrees
For the green ray
sin Ar = 0.4843 Ar = 28.97 degrees
Take the difference
To solve this problem, we need to use Snell's law, which relates the angles and refractive indices of incident and refracted light at a boundary between two different media.
Snell's law is given by: n1*sin(theta1) = n2*sin(theta2)
Where:
- n1 and n2 are the refractive indices of the media.
- theta1 and theta2 are the angles that the incident and refracted rays make with the normal to the surface, respectively.
In this case, we have two different wavelengths and corresponding refractive indices for fused quartz:
- For indigo light (400 nm), n1 = 1.47.
- For green light (550 nm), n2 = 1.46.
Since both rays enter at the same angle of 45º, we can assume that theta1 = theta2 = 45º.
We need to find the angle that separates the two rays as they travel through the fused quartz. Let's call it delta_theta.
Using Snell's law, we can rewrite it as: sin(theta2) = (n1/n2) * sin(theta1)
Now, we can substitute the values and solve for sin(delta_theta):
For indigo light:
sin(theta2_indigo) = (1.47/1.46) * sin(45º)
For green light:
sin(theta2_green) = (1.46/1.47) * sin(45º)
To find the angle that separates the two rays, we need to find the difference between theta2_indigo and theta2_green:
delta_theta = theta2_indigo - theta2_green
Finally, we can convert delta_theta to degrees and find the closest option among the given choices.
By performing the calculations, the angle that separates the two rays as they travel through the fused quartz is closest to 0.37º.