Angular seperation between diff wavelengths

In summary, the conversation discusses the incident of a ray of light with blue and red wavelengths on a piece of glass at a certain angle and the calculation of the angular separation between the refracted red and blue beams while they are in the glass. The respective indices of refraction for the blue light and red light are also mentioned. The individual asks for help and is advised to treat the problem as two separate cases and calculate the angles of refraction for each, then find the difference to determine the angular separation.
  • #1
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 :wink:
 
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  • #2
Just treat it as two different problems. If you have monochromatic light incident on a surface at an angle θi, how do you calculate the angle of refraction θr? Do that for both cases, and subtract the two angles to find the angular separation.
 
  • #3

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!
 

1. What is angular separation between different wavelengths?

The angular separation between different wavelengths refers to the difference in the direction or position of two or more wavelengths of light as observed from a particular point. It is typically measured in degrees or radians and can be used to describe the distance between two objects or the spread of a spectrum of light.

2. How is angular separation between different wavelengths calculated?

The angular separation between different wavelengths can be calculated using trigonometry. It involves using the distance between the two objects or the width of the spectrum and the wavelength of the light to determine the angle of separation. The formula for calculating angular separation is: θ = λ/d, where θ is the angular separation, λ is the wavelength, and d is the distance or width.

3. What is the significance of angular separation between different wavelengths?

The angular separation between different wavelengths is significant because it can provide information about the distance between objects, the size of objects, and the properties of light such as its wavelength and frequency. It is also used in various fields of science, including astronomy, physics, and optics, to study and understand the behavior of light and its interactions with matter.

4. How does angular separation between different wavelengths affect the appearance of objects?

The angular separation between different wavelengths can affect the appearance of objects in several ways. The angle of separation can determine the color of an object, as different wavelengths of light correspond to different colors. It can also affect the apparent size of an object, as a larger angular separation can make an object appear larger. Additionally, the angle of separation can affect the brightness or intensity of an object, as it determines the amount of light received from the object.

5. Can angular separation between different wavelengths change?

Yes, angular separation between different wavelengths can change. It can change when the distance between objects changes, when the wavelength of light changes, or when the angle of observation changes. In astronomy, the angular separation between objects can also change due to the movement of celestial bodies, such as the Earth's orbit around the Sun. In general, any change in the factors that affect the calculation of angular separation can result in a change in its value.

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