Write the single-slit intensity formula in terms of \(\beta\).

Define \(\beta\) for a single-slit diffraction pattern.

What is the value of \(I/I_0\) at \(\beta=0\)?

Find \(I/I_0\) when \(\beta=\pi/2\).

Find \(I/I_0\) when \(\beta=\pi\).

What values of \(\beta\) give single-slit intensity minima?

Show that \(\beta=m\pi\) gives \(a\sin\theta=m\lambda\).

Why is the single-slit intensity pattern symmetric about \(\theta=0\)?

For \(a=0.20\,\mathrm{mm}\), \(\lambda=500\,\mathrm{nm}\), and \(\theta=1.25\times10^{-3}\,\mathrm{rad}\), find \(\beta\).

Using the result of question 9, find \(I/I_0\).

Why are side maxima in a single-slit pattern much weaker than the central maximum?

At a single-slit minimum, does the electric field amplitude or only the intensity vanish?

A point has \(\beta=3\pi\). What is the intensity?

Find \(I/I_0\) when \(\beta=3\pi/2\).

What is wrong with substituting \(\beta=0\) directly into \(\sin\beta/\beta\)?

A single-slit minimum is observed when \(\beta=2\pi\). What minimum order is this?

Explain why the intensity formula contains a square.

A measurement gives \(I/I_0=0\) at \(\theta=4.0\times10^{-3}\,\mathrm{rad}\) for the first minimum. If \(a=0.150\,\mathrm{mm}\), estimate \(\lambda\).

If \(a\) is increased while \(\theta\) and \(\lambda\) are fixed, what happens to \(\beta\)?

Why can the single-slit intensity formula be described as a continuous version of many-source interference?