Light Waves and Colors Legacy Problem #15 Guided Solution
Problem*
Mr. H’s period 7 physics class is attempting to duplicate Thomas Young’s experiment in which they use a two-point source light interference pattern to measure the wavelength of light. They shine red laser light through a slide containing a double slit; the slit spacing is 0.125 mm. The light interference pattern created by the light which passes through the slits is projected on a screen a distance of 10.72 m away. Justin and Shirley measure the distance from the 3rd antinodal bright spots on opposite sides of the pattern to be 33.9 cm apart. Based on these measurements, what is the wavelength of the red laser light.
Audio Guided Solution
This problem pertains to the Young's experiment and the use of the Young's equation to determine the wavelength of light from a two-point source light interference pattern. The mathematics of Young's equation and Young's experiment are discussed at the physics classroom tutorial and clicking the link that you see at the bottom of this page will lead you back to some understandable information about that experiment. Now here we have to calculate the wavelength and we are given four quantities. The quantities that we are given are y, d, m, and l. The l is the distance from the slits or the sources of light to the screen where the pattern is projected and it is 10.72 meters. The d is the distance between the two sources or slits through which the laser light is shown and it is 0.125 millimeters. Y and m are perhaps among the most difficult things to determine in problems such as this and if we are measuring from the third antinodal line on opposite sides of the patterns what we are doing is measuring six different spacings between antinodal lines. So the m value is six and the y value that goes with it is 33.9 centimeters and the equation that relates these four variables to the wavelength of light is lambda for wavelength is equal to y times d divided by m divided by l. So now we know all four quantities and you would think it would be easy enough just to substitute into the equation and solve for lambda but before you do you need to give great attention to units and my recommendation is especially if you are having difficulties with unit convergence is to take all the quantities and convert them to the same unit then substitute into the equation and solve for wavelength and the unit I would suggest is the unit meters. If you are not having difficulty with converting units then you probably do not need my suggestion at all. So what I am going to do is convert the d of 0.125 millimeters to meters that comes out to be 0.000125 and I am going to convert the y to meters as well so that 33.9 centimeters becomes 0.339 meters. L is already in meters and m is unit less. So now that I have my quantities expressed in meters I am going to substitute it into Young's equation. So I say wavelength equals 0.339 meters times 0.000125 meters divided by 10.72 meters divided by 6 and this gives me 6.5882 times 10 to the negative 7th meters and I can round that to three significant digits 6.59 times 10 to the negative 7th meters. Converting to nanometers means I have to multiply this number by 10 to the 9th and that gives me 659 nanometers.
Solution
6.59x10-7 m or 659 nm
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.