what angle do blue light wavelength of 460 nm and red light 680 nm disperse upon entering from vacuum to a dispersion medium with n(blue)=1.349 and n(red)=1.213 at an incident angle of 20 degree?
To calculate the angle at which blue and red light wavelengths disperse upon entering a dispersion medium, we can use the equation of Snell's Law:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
- n₁ and n₂ are the refractive indices of the medium for blue and red light respectively.
- θ₁ is the incident angle (20 degrees in this case).
- θ₂ is the angle at which the light is dispersed.
First, let's calculate the angle of refraction for blue light (460 nm):
n(blue) = 1.349
θ₁ = 20 degrees
Rearranging Snell's Law equation, we have:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
substituting the values:
sin(θ₂) = (1.349 / 1) * sin(20)
sin(θ₂) ≈ 1.349 * 0.342
θ₂ = arcsin(0.4617)
θ₂ ≈ 27.87 degrees
Therefore, the blue light with a wavelength of 460 nm would disperse at an angle of approximately 27.87 degrees when entering the dispersion medium.
Now, let's calculate the angle of refraction for red light (680 nm):
n(red) = 1.213
θ₁ = 20 degrees
Using the same equation:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
substituting the values:
sin(θ₂) = (1.213 / 1) * sin(20)
sin(θ₂) ≈ 1.213 * 0.342
θ₂ = arcsin(0.4156)
θ₂ ≈ 24.76 degrees
Therefore, the red light with a wavelength of 680 nm would disperse at an angle of approximately 24.76 degrees when entering the dispersion medium.