Light Waves and Colors Legacy Problem #18 Guided Solution
Problem*
Maria and Jason are doing the same lab as Jackson and Melanie (from the previous problem). Maria and Jason determine the distance between the central bight spot and the 4th bright spot to be 29 cm. The distance from their slide to the whiteboard (where the interference pattern is projected) is 2.76 m. The slits in their slide are also spaced 25 micrometers apart. Based on Maria and Jason’s measurements, what is the wavelength of the red laser light (in nanometers)? (GIVEN: 1 m = 106 mm, 1 m = 109 nm)
Audio Guided Solution
Here, Maria and Jason are trying to do Young's experiment. In Young's experiment, light from a source passes through two slits to create an interference pattern. The pattern is projected onto some sort of screen. Measurements are made in such a manner as to calculate wavelength using Young's equation, wavelength equal yd over ml. In this particular experience, Maria and Jason are measuring a distance on the screen from the central bright spot to the fourth bright spot. This is a distance of 29 centimeters and is represented by y in Young's equation. So I say y equal 29 centimeters. Now the m value that goes with this y value is equal to 4 because Maria and Jason are measuring from the central bright spot out to the fourth bright spot and that's equivalent to four spacings between bright spots. The distance from their slide to the whiteboard is 2.76 meters and this represents l. So I say l equal 2.76 meters. And finally, the slits on the slide through which the laser light is shown are separated by 25 micrometers. So I say d equal 25 micrometers. Now I know everything I need to know in order to calculate wavelength using Young's equation. Only problem is that I need to get consistent units. So I'm going to convert everything to meters, which means I need to take the y value of 29 centimeters and convert that to 0.29 meters. And I need to take the d value of 25 micrometers and convert that to meters. So it becomes 2.5 times 10 to the negative 5th meters when I divide by 10 to the 6th. Now I take my values of y, d, m, and l and I substitute it into Young's equation. And in doing so, I'm going to go y of 0.29 meters multiplied by d of 2.5 times 10 to the negative 5th meters divided by m of 4 divided by l of 2.76 meters. When I do the math, I get 6.567 times 10 to the negative 7th meters, and I need to convert that to nanometers as requested. So I multiply by 10 to the 9th. That gives me 656.70 nanometers, and I can round to two significant digits such that it becomes 660 nanometers.
Solution
660 nm (rounded from 657 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!
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