What is the width of the slit?

Question

Light of wavelength 603.0 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 70.5 cm from the slit. The distance on the screen between the third order minimum and the central maximum is 1.09 cm.

 

What is the width of the slit?

 

I keep getting this question wrong and am not sure what part of my work is wrong or if I'm using the wrong formula. Writing out the steps would be very helpful! 

Answer 1

Hi Payton!

 

You should be using the expression for distance along the screen from the center maximum to the mth minimum on one side:

 

y = mDλ/a

 

where

 

a = width of slit

D = distance to screen

λ = wavelength of light

m = order number (the number of the minimum you are dealing with)

 

In this case, you want to solve for a, so we can rearrange the above expression into:

 

a = mDλ/y

 

You can just drop in your given values.  Remember to make all length units (for y, D, and λ) the same.  If we convert them all to meters, for example, we should have:

 

y = 0.0109 m

D = 0.705 m

λ = 603 x 10^-9 m

and m = 3

 

Solving for a with these values should give you a in meters.  

 

Hopefully, that helps out, and lets you get unstuck.  If you would like to check an answer or have any other questions about this, just let me know!