Double, single slit, and diffraction

[jhonny09]

Homework Statement

Hi guys,
I'm going through a rough time understanding double and single slit and diffraction.

Here's the first problem:
A) A single slit gives destructive interference when m*L=w*sin(theta). A double slit gives constructive interference when m*L=d*sin(theta). Explain the role of d and w for the double and single slit.

B) A very wide slit is narrowed to zero width. When(at what point)does diffraction start to occur?

Homework Equations

A) I guess we can just use the above equations to figure out what their roles are.

B) I was thinking to use a*sin(theta)=m*L

The Attempt at a Solution

A) I don't know how to explain and how those two are related to each other

B) I guess I could say that diffraction starts to occur when a>0, but I'm not sure because it wants a specific point.

Thank you,
Jhonny

 

[anathema]

Hi Jhonny,

I understand your struggles with understanding double and single slit diffraction. I will try my best to explain the roles of d and w for the double and single slit.

For the single slit, the equation m*L=w*sin(theta) represents the conditions for destructive interference. Here, w represents the width of the slit and L represents the distance between the slit and the screen. This equation tells us that when the sine of the angle of diffraction (theta) is equal to a whole number multiple of the wavelength (m), destructive interference will occur. This means that the waves passing through the slit will cancel each other out, resulting in a dark spot on the screen.

For the double slit, the equation m*L=d*sin(theta) represents the conditions for constructive interference. Here, d represents the distance between the two slits. This equation tells us that when the sine of the angle of diffraction (theta) is equal to a whole number multiple of the wavelength (m), constructive interference will occur. This means that the waves passing through the two slits will add together, resulting in a bright spot on the screen.

In summary, the role of d and w in the double and single slit is to determine the conditions for constructive and destructive interference, respectively. The distance between the slits (d) and the width of the single slit (w) affect the angle of diffraction and determine whether constructive or destructive interference will occur.

For your second problem, you are on the right track. Diffraction occurs when the width of the slit (a) is greater than zero. However, to find the specific point at which diffraction starts to occur, you can use the equation a*sin(theta)=m*L. This equation tells us that when the width of the slit is equal to the wavelength, diffraction will start to occur. This is because at this point, the waves passing through the slit will start to spread out and interfere with each other.

I hope this helps clear up some of your confusion. Let me know if you have any other questions.