Single slit diffraction, from an angle

[mooshasta]

I've encountered a standard problem about single slit diffraction, but there's a slight change to the problem and I don't know how it should be dealt with.

The question is:

A plane wave of 400-nm light is incident on a 25-µm slit in a screen, as shown in the figure below. At what incident angle will the first null of the diffraction pattern be on a line perpendicular to the screen?

http://www.tubaroo.com/ssd.PNG
I know the equation for the minima in a single slit diffraction problem is $\sin \theta = m \frac{\lambda}{d}$ where $m$ is 1,2,3,... and $d$ is the width of the slit. I want to say that the question is not as tricky as I'm making it out to be, and that I should just solve for $\theta$ using that equation. But if this were the case, it seems to me that since the light is coming from an angle, the effective width of the slit should be smaller, or something along those lines. I've scoured the internet for this type of situation, but every time I see the single slit diffraction problem, the angle of incidence of the light is 0 degrees.

Can anyone help me out?

 

[Hootenanny]

Just reverse the problem. Treat the porblem as if the light was traveling in the opposite direction and apply your formulae as you would normally.

 

[kyle8921]

I can offer some insight into this problem. First, it is important to note that the equation for the minima in single slit diffraction is derived assuming a normal incidence of light, meaning the light is coming in perpendicular to the slit. In this case, with an incident angle, the effective width of the slit will indeed be smaller, but it is not a simple decrease in width. The effective width will depend on the angle of incidence and the actual width of the slit.

To solve this problem, you can use a modified version of the equation you mentioned. Instead of using the actual width of the slit, you can use the effective width, which can be calculated using the actual width and the angle of incidence. This will give you a new equation to solve for the angle at which the first null occurs. However, this approach may not be accurate for small angles and may require a more complex mathematical approach.

Alternatively, you can use a simulation or software to model the diffraction pattern for this specific scenario. This will provide a more accurate result, taking into account the angle of incidence and the actual width of the slit.

In conclusion, the standard equation for single slit diffraction may not be directly applicable in this case and a modified approach or the use of simulation may be needed to accurately solve the problem. I hope this helps in your understanding of the single slit diffraction phenomenon.