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

[newguy_13]

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

 

[RPinPA]

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/