C.3.13 (HL)—Diffraction envelope

Separate the two patterns

In a multiple-slit intensity pattern, the fine interference maxima are contained within a broad single-slit diffraction envelope. The envelope sets the overall intensity scale; the double-slit or multiple-slit interference determines the rapid fringe structure.

Relate the widths

The single-slit envelope depends on slit width $b$ , while the separation of fine interference maxima depends on source or slit separation $d$ . A smaller $b$ makes the envelope wider; a larger $d$ makes interference fringes closer together.

Explain missing or unequal maxima

Interference maxima at different angles can have different intensities because the envelope changes across the screen. Some interference maxima may fall at an envelope minimum and disappear.

Common trap

Do not treat every interference maximum as having the same height, and do not confuse the fine fringe spacing with the width of the single-slit envelope.

[ 1 ]

Light of wavelength $\lambda$ is incident on two parallel slits of width b that are separated by distance d. The graph of intensity against diffraction angle is shown.

diffraction angle/rad

What are $\frac{\lambda}{d}$ and $\frac{\lambda}{b}$ ?

$\frac{\lambda}{d}$

$\frac{\lambda}{b}$

0.1

0.01

0.1

0.01

The HL extension is secure when you can model diffraction as interference and read the limits of the pattern.

Single-slit diffraction: b sinθ = nλ for minima
Diffraction envelopes in multiple-slit patterns
Diffraction grating maxima: nλ=d sinθ
Allowed orders satisfy nλ≤d

C.3.13 (HL)—Diffraction envelope

Read the Diffraction Envelope

Retrieve the HL C.3 Wave Phenomena Model

C.3.13 (HL) Exam Analysis