With the info given, what are 3 ways to calculate wavelength?

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In summary, the wavelength of light was determined through three different methods: using the angle to the third dark fringe, the distance from the slits to the screen, and the distance between the first and third maximum. The resulting wavelength was found to be 7.56x10^-7m.
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Homework Statement


In an investigation into single-slit diffraction, a laser is used to produce an interference pattern on a screen. With the following information determine the wavelength of the light in 3 different ways.
· The angle to the third dark fringe is 2.6˚.

· The distance from the slits to the screen is 3.00 m.

· The distance from the center of the central maximum to the second dark fringe is 9.0740 cm.

· The distance from the first maximum to the third maximum is 9.072 cm.

· The width of the slit is 0.0500 mm.

Homework Equations


I know it is a single slit problem therefore:
sintheta=(n)(wavelength)/(w)
y/L=(n)(wavelength)/(w)
Don't know the 3rd

The Attempt at a Solution


Sin(theta)=n(wavelength)/w
Sin(theta)(w)/n=wavelength
Wavelength=(sin2.6)(5.0x10^-5)/3
Wavelength=7.56x10^-7m

y/L=(n)(wavelength)/w
wavelength=wy/nL
wavelength=(5.0x10^-5)(0.09074)/2(3)
wavelength=7.56x10^-7m

I don't know the 3rd equation
Thanks for the help
 
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newguy_13 said:
I know it is a single slit problem therefore:
sin(theta)=(n)(wavelength)/(w)

That is the equation for the location of the minima, the dark fringes, and since you were told the location of the 2nd and 3rd dark fringes, you can use that equation with n = 2 and n = 3 as you did.

You were given one more piece of independent information: "The distance from the first maximum to the third maximum is 9.072 cm". That's your 3rd piece of information and the source of your 3rd equation. I'd approximate the maxima as being halfway between the minima. So the first is at n = 1.5 and the third is at n = 3.5. You weren't given the values of y for these two maxima, but you were given the difference. So write down the expression for ##y_1## and for ##y_2## with those two values of n, and subtract.

By the way, this forum supports constructing equations in the math typesetting language called LaTeX. Basic guide here: https://www.physicsforums.com/help/latexhelp/
 

1. What is the formula for calculating wavelength?

The formula for calculating wavelength is: wavelength = speed of light / frequency. This formula is also known as the wave equation.

2. How do you calculate wavelength using the wave equation?

To calculate wavelength using the wave equation, you need to know the speed of light (c) and the frequency (f). The formula is: wavelength = c / f.

3. What is the relationship between wavelength and frequency?

Wavelength and frequency are inversely proportional to each other. This means that as wavelength increases, frequency decreases, and vice versa. This relationship is described by the wave equation, where c (speed of light) is constant.

4. Can wavelength be measured directly?

No, wavelength cannot be measured directly. It is a calculated value that depends on the speed of light and frequency, which can be measured using specialized instruments.

5. Are there other ways to calculate wavelength?

Yes, there are two other ways to calculate wavelength: using the energy of a photon and using the momentum of a particle. These methods are based on the wave-particle duality of light and are commonly used in quantum mechanics.

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