How wide is a single slit that gives its first minimum at 90°?

[jmacmartin]

Homework Statement

How wide is a single slit that gives its first minimum at 90°?

Homework Equations

øp=p(λ/a)

The Attempt at a Solution

Not quite sure what the answer is looking for but I'd guess I would need to solve for "a." So...

90°=(λ/a)


Is there any more information I can gather from this problem? Any guidance would be a big help.

Thanks guys!

 

[BvU]

Hello JMM and welcome to PF,

The answer isn't looking for anything. You've given a problem statement, but suppose I didn't know any of the symbols appearing in your equation; then: how could I help you ?

Do you know what the answer is to "How wide is a single slit that gives its first minimum at 30°?" or 45 or 60 ? Can you express that in a formula ? Then moving on to 90 shouldn't be too dificult, right ? Or... ?

 

[jmacmartin]

Hi BvU,

I do not know the answer to that question. No matter the angle, I'm not quite sure how to express it in a formula. I apologize if I have not asked my question in the proper form for this website.

I know the equation øp=p(λ/a) will tell me where the dark bands are on the screen. I assume øp = 90 since that is given. I do not know λ. It appears I need to solve for a, which is the width of the slit.

 

[BvU]

Let me rephrase:
What is ø and what are the units ?
What is p and what are the units ?
What is λ (ok, the wavelength in m)
What is a and what are the units ? Ah we know now: the width of the slit. Also in m.

Your expression doesn't look like what I see coming by when I simply google the title of this post. So it comes from your book or your notes, right ? What is it based on ?
(Note that in many treatments a small-angle approach is used, where $\sin\theta=\tan\theta=\theta$. This is something you can't have in this exercise!)

In an exercise like this, it is OK to express the answer in units of λ .

Oh, and:

I know the equation øp=p(λ/a) will tell me where the dark bands are on the screen

makes me wonder where in the equation the multiplicity ("dark bands") appears?

 

[jmacmartin]

Sorry to waste your time with stupid questions. I will seek help elsewhere.

 

[BvU]

I'm fully prepared to provide the best possible assistance. But your cooperation is indispensible.