A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 81.0°. The index of refraction of quartz is 1.455 at 660 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.
37. A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence
of 50.0°. The index of refraction of quartz is 1.455 at 600 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.
To find the dispersion of the slab, we need to find the difference in the angles of refraction for the red and violet light.
The angle of incidence is given as 81.0°. The indices of refraction for red and violet light are given as 1.455 and 1.468, respectively.
To find the angle of refraction, we can use Snell's Law, which states:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
- n₁ and n₂ are the indices of refraction for the two media
- θ₁ is the angle of incidence
- θ₂ is the angle of refraction
For red light:
n₁ = 1.455
n₂ = 1 (since air has an index of refraction close to 1)
θ₁ = 81.0° (given)
We can rearrange Snell's Law to solve for θ₂ for red light:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
θ₂ (red) = arcsin((n₁ / n₂) * sin(θ₁))
For violet light:
n₁ = 1.468
n₂ = 1 (same as air)
θ₁ = 81.0° (same as angle of incidence for red light)
Similarly, we can find θ₂ for violet light:
θ₂ (violet) = arcsin((n₁ / n₂) * sin(θ₁))
Finally, we can calculate the dispersion by finding the difference between θ₂ for red and violet light:
Dispersion = θ₂ (violet) - θ₂ (red)
Plug in the values into these formulas to find the dispersion of the slab.