Single slit diffraction - distance between 1st&2nd order dark fringes

[louza8]

Homework Statement

Monochromatic light with wavelength 580nm passes through a single slit 2.60um wide and 2.10m from a screen.

Find the distance between the first- and second-order dark fringes on the screen.

Homework Equations

y=(n*lamda*L)/d

The Attempt at a Solution

y1=580nm*2.1m/2.1um=0.468m
y2=580nm*2.1m*2/2.1um=0.937m

y2-y1=0.468m

I am not sure how to handle the dark fringes in single slit diffraction, so I am not sure where I am going wrong.

Thanks for people's help in advance.

 

[ehild]

Do you know what the letters mean in the formula y=(n*lambda*L)/d and when is it a good approximation?

ehild

 

[louza8]

y is the distance between the fringes hitting the screen, n is the order, lambda is the wavelength, L is the distance to the screen, d is the width of the slit?

i don't know when it is a good approximation or what you mean by that.

 

[ehild]

Yo know a formula which contain the angle of deviation from the original direction of the light ray, hitting the slit. It is the exact one. ehild

 

[louza8]

n*lamda = d*sin(theta) ?

so would i use the angle found theta, and the known length L in a triangle to find the difference in y?

 

[ehild]

Yes. Calculate theta for n=1 and for n=2. The relation between L and y is y/L=tan(theta). If theta was very small, not more than a few degrees, you could approximate sin(theta) with tan(theta) and the equation in your first post would be valid. It is not the case now.

ehild

 

[louza8]

thanks ehild, helpful as always