Light Waves and Colors Legacy Problem #19 Guided Solution
Problem*
Jill is helping her younger brother Nathan set up an exhibit for a Science Fair. Nathan’s exhibit pertains to the wave-particle nature of light waves. He wishes to demonstrate the wave nature of light by displaying the two-point interference pattern of red laser light (λ = 648 nm). Nathan has purchased a double slit slide from a science warehouse which has slits separated a distance of 0.125 mm. Nathan has asked Jill to determine the slide-to-screen distance which will result in a 2.0 cm separation between adjacent bright spots. What distance will result in this antinodal spacing?
Audio Guided Solution
Nathan is using a two-point source interference pattern for a science fair project. What he wishes to do is shine red laser light through some slits which he has purchased and then project the interference pattern onto a screen such that the distance between adjacent bright spots is about two centimeters. So Nathan asks his sister Jill to help him out with the calculations. So what Jill needs to do is to calculate an L distance using Young's equation, wavelength equal Y times D over M times L. And what we know is that the wavelength is equal to 648 nanometers. We know that the distance between the slits which the laser has shown is 0.125 millimeters, that's D equal 0.125 millimeters, and we know that Y is equal to 2.0 centimeters when the M value is equal to 1. So if we're going to solve for the distance L, we need to take Young's equation and rearrange it so as to solve for L. That equation would rearrange to L equal Y times D divided by M divided by L. All we have to do now is to make sure all our quantities are in the same units. And I'm going to pick meters as my unit to convert to. So my 648 nanometers for lambda becomes 6.48 times 10 to the negative 7th meters. And my D of 0.125 millimeters becomes 1.25 times 10 to the negative 4th meters. And my Y of 2.0 centimeters becomes 0.020 meters. Now I can substitute these quantities into the Young's equation that's been rearranged and I end up solving for L and it becomes 3.858 meters. I can round that to two significant digits so that it's 3.9 meters.
Solution
3.9 m
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Light Waves and Colors at The Physics Classroom Tutorial.