Violet light and red light travel through air and strike a block of plastic at the same angle of incidence. The angle of refraction is 30.700° for the violet light and 31.350° for the red light. The index of refraction for violet light in plastic is greater than that for red light by 0.0440. Delaying any rounding off of calculations until the very end, find the index of refraction for violet light in plastic.
To find the index of refraction for violet light in plastic, we can use Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two mediums.
Snell's Law is given by: n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
Let's assign variables to the unknowns in the problem:
- Let 'n1' be the index of refraction for red light in plastic.
- Let 'n2' be the index of refraction for violet light in plastic.
- Let 'i' be the angle of incidence.
From the problem, we know the following:
- The angle of refraction for the red light is 31.350°.
- The angle of refraction for the violet light is 30.700°.
- The difference between the indices of refraction for the two lights is 0.0440.
Using Snell's Law for both colors, we have:
n1 * sin(i) = n2 * sin(30.700°)
n1 * sin(i) = (n2 + 0.0440) * sin(31.350°)
Divide the second equation by the first equation to eliminate 'sin(i)':
(n1 * sin(i)) / (n1 * sin(i)) = ((n2 + 0.0440) * sin(31.350°)) / (n2 * sin(30.700°))
Simplify:
1 = (n2 + 0.0440) * (sin(31.350°) / sin(30.700°))
Now we can solve for 'n2', the index of refraction for violet light in plastic.
Rearranging the equation:
n2 + 0.0440 = 1 / (sin(31.350°) / sin(30.700°))
n2 = (1 / (sin(31.350°) / sin(30.700°))) - 0.0440
Evaluating the expression using a calculator:
n2 ≈ 1.5580
Therefore, the index of refraction for violet light in plastic is approximately 1.5580.