How a prism separates colors

Job #3: How a prism separates blue light from red light

A prism breaks up the colors in white light because the index of refraction, n, of any glass is different for different colors (different wave lengths of light).

Suppose that a ray of white light enters one side of an equilateral prism (60° 60° 60°) as shown in the picture below. You will calculate the angle which separates the blue from the red ray as they emerge from the far side of the prism.
The key to the working of the prism is that the index of refraction of any one type of glass is different for different colors. The glass of which the prism of this problem is made has an index of refraction of 1.51 for red and 1.53 for blue light.

(a) First calculate the velocity of the light of each color in this glass. Note: c=3.0×(10E8)m/sec

Equation
that you used:

light velocity (red) = _____________m/sec
light velocity (blue) = ____________m/sec

(b) Now, assuming that a ray of white light, containing both red and blue parts, enters the prism at an angle, "a", [measured, as usual, between the ray and the perpendicular]

Given that angle "a" = °

first, calculate just the two angles, b(Blu) and b(Red) made by the rays after they enter the prism. Keep 2 decimal places in the calculation of all angles.

Equation that you used:

Find first the sine of the angles, then the angles themselves. What did you get?

sin b(red) = __________	sin b(blu) = __________
b(red) = __________°	b(blu) = __________°

(c) The next step requires the use of a little geometry: find (for each color) the angles c on the far surface of the prism, and d as the rays leave the glass and go back into air. [Don't forget that the angles are always measured to the dashed lines that are perpendicular to the glass/air surface]
The angle, c, is of course determined by the angle, b, and the 60° angle at the top of the prism.
Using the diagram at the left, using the angles B and C, derive a relation between angle c and angle b:

angle B + angle C + 60° = ________°

but, also the following are true:
angle B = 90° - angle_______
and
angle C = 90° - angle_______

Now substitute the two lower expressions for B and C, into the top relation; what do you get?

Simplify this to give you an expression for angle c in terms of angle b

angle c = _____________________________________

Use this expression to find the angles c for the red and blue rays:

angle c(Red) = _____°

angle c(Blu) = _____°

(d) Now, use the same method as in (b) [except remember that the ray is now going from glass into air] to find the angles, d for both the red and blue rays.

sin d(red) = __________	sin d(blu) = __________
d(red) = __________°	d(blu) = __________°

Finally, the the angle between the red and blue rays as they emerge from the prism is given by the difference between angle d(red) and angle d(blu)

The angle of separation between red and blue light due to this prism is _______°

Back to Job #1: Sally and Kenny go Wading
Back to Job #2: The famous fishing pole paradox
On to Job #4: The World's First Camera, or, How the Human Eye Works
On to Job #5: The Telescope, or How the Dutch Lens Grinders Made Galileo Famous
On to the Telescope Lab: Take two lenses and make a telescope right there in the lab
Answers to "Job" problems
Back to Optics Main menu

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