Diffraction Problem, Calculate Slit Width

[TheRedDevil18]

Homework Statement

Light of wavelength 680nm falls onto a single slit. The diffraction pattern is observed on a screen 50cm away. If the distance between the first and the third minima is 3mm, calculate the slit width?

Homework Equations

sin thetha = m*lambda/a
y = m*lambda*R/a

The Attempt at a Solution

So the distance between the first position and last position of the dark band is 3mm?

I think this is wrong:

3*10^-3 = (3)(680*10^-9)(0.5)/a
a = 3.4*10^-4 m

 

[Redbelly98]

Homework Equations

sin thetha = m*lambda/a
y = m*lambda*R/a

The Attempt at a Solution

So the distance between the first position and last position of the dark band is 3mm?

I think this is wrong:

3*10^-3 = (3)(680*10^-9)(0.5)/a
a = 3.4*10^-4 m

There are a couple of issues with your attempt.

1. It looks like you have inserted an extra factor of 0.5 for no apparent reason.

2. Without the 0.5, the formula gives the spacing between the 3rd minimum and the central maximum.
However, the 3 mm given in the problem statement refers to the spacing between the 3rd minimum and the 1st minimum. So you need to bring the 1st minimum (n=1) into the picture.