Destructive interference through a narrow slit

[JoeyBob]

Homework Statement:

See attached

Relevant Equations:

angle=wavelength/a

So I thought angle=wavelength/width of slit

But when I solve for the width I got the wrong answer of 4567 nm, when the answer is suppose to be 130881 nm. I figured out that I needed to multiply my incorrect answer by 28.7, but where does this constant come from? Its not part of the equation when there's constructive interference.

 

[anuttarasammyak]

It might be half of coefficient between degree and radian
$$360 / 2\pi = 57.29..$$

 

[JoeyBob]

It might be half of coefficient between degree and radian
$$360 / 2\pi = 57.29..$$

How does that convert to multiplying wavelength/angle by 28.7?

 

[anuttarasammyak]

This coincidence hinted me that you might have used angle value of degree not radian in the calculation. How did you do it?

 

[JoeyBob]

This coincidence hinted me that you might have used angle value of degree not radian in the calculation. How did you do it?

Youre right, not used to seeing degrees so small. But when I convert it to radians I now have to divide the answer I get by 2 to get the right answer, why is that?

width = wavelength/angle = 540 nm /0.00209 radians, but this gives me an answer that needs to be divided by 2 to get the right answer.

 

[anuttarasammyak]

For enhanced interference
$$d\sin\theta=\lambda$$
For destructive interference
$$d\sin\theta=\frac{\lambda}{2}$$
, a half of the former.