Answer :
The problem you've described involves the refraction of light, specifically Snell's Law, which explains how light bends when it moves from one medium to another.
Snell's Law
Snell's Law is given by the equation:
[tex]n_1 \sin(\theta_1) = n_2 \sin(\theta_2)[/tex]
- [tex]n_1[/tex] is the refractive index of the first medium (in this case, air, which has a refractive index of approximately 1).
- [tex]\theta_1[/tex] is the angle of incidence, which is 55.0 degrees in this case.
- [tex]n_2[/tex] is the refractive index of the second medium (glass, in this case), which affects different wavelengths of light differently, leading to the phenomenon of dispersion.
- [tex]\theta_2[/tex] is the angle of refraction, which is 37.1 degrees for red light and 35.7 degrees for violet light.
Calculating Refractive Indices
For Red Light:
Rearrange Snell's Law to solve for [tex]n_2[/tex]:
[tex]n_2 = \frac{n_1 \sin(\theta_1)}{\sin(\theta_2)}[/tex]
Substitute the values for red light:
[tex]n_2 = \frac{1 \cdot \sin(55.0^\circ)}{\sin(37.1^\circ)}[/tex]
Calculate using a scientific calculator or appropriate software to find this value.For Violet Light:
Similarly, rearrange and substitute in the values for violet light:
[tex]n_2 = \frac{1 \cdot \sin(55.0^\circ)}{\sin(35.7^\circ)}[/tex]
Calculate this value as well.
Why This Happens
- Dispersion: Different colors (wavelengths) of light refract by different amounts. This is due to the wavelength-dependent nature of the refractive index.
- Result: This is why red and violet light refract at different angles in the same medium.
I hope this step-by-step explanation helps you understand how light behaves when it moves from one medium to another, and how Snell's Law can be used to find refractive indices based on angles of incidence and refraction! If you're using a calculator, ensure it's set to the correct mode (degrees) for accurate calculations.
