Angular seperation between diff wavelengths

[Dx]

A ray of light consists of blue light(480nm wavelength) and red light(670nm wavelength) is incident on a think piece of glass at 80 degrees. what is the angular separation between the refracted red and blue beams while they are in glass? (The respective indices of refraction for the blue light and red light are 1.4636 and 1.4561)

What in the hell do I do?

I have got no clue what to do here, please help. Lost soul here with lots of determination to learn without using a lot of math. HEHEHE!
Any help would be appreciated!
Thanks!
Dx

 

[quantumdude]

Just treat it as two different problems. If you have monochromatic light incident on a surface at an angle θ_i, how do you calculate the angle of refraction θ_r? Do that for both cases, and subtract the two angles to find the angular separation.

 

[M98Ranger]

Hi there! Don't worry, I can help you out with this problem.

First, we need to understand what angular separation means. Angular separation is the angle between two rays of light after they have been refracted (or bent) by a medium, in this case, the glass.

To find the angular separation between the red and blue beams, we need to use Snell's law, which 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 speed of light in the first medium to the speed of light in the second medium.

In this case, we have the angle of incidence (80 degrees) and the indices of refraction for the blue and red light. We can use these values to find the angle of refraction for each beam.

For the blue light:
sin(80 degrees)/sin(angle of refraction for blue) = speed of light in air/speed of light in glass
sin(angle of refraction for blue) = sin(80 degrees) * speed of light in glass/speed of light in air
sin(angle of refraction for blue) = sin(80 degrees) * 1.4636/1
sin(angle of refraction for blue) = 0.9946
angle of refraction for blue = 81.13 degrees

For the red light:
sin(80 degrees)/sin(angle of refraction for red) = speed of light in air/speed of light in glass
sin(angle of refraction for red) = sin(80 degrees) * speed of light in glass/speed of light in air
sin(angle of refraction for red) = sin(80 degrees) * 1.4561/1
sin(angle of refraction for red) = 0.9927
angle of refraction for red = 81.03 degrees

Now, we can use these angles to find the angular separation between the two beams. We simply subtract the angle of refraction for red from the angle of refraction for blue.

Angular separation = 81.13 degrees - 81.03 degrees = 0.10 degrees

So, the angular separation between the refracted red and blue beams while they are in glass is 0.10 degrees.

I hope this helps! Feel free to ask for clarification if you need it. Keep up the determination to learn, you got this!