A laser shines through a slit of width a and produces a diffraction pattern on a screen. The slit is then narrowed to a/2. What happens to the central maximum?
AIt becomes narrower, because less light passes through and the beam is more concentrated
BIt stays the same width, since the wavelength of light hasn't changed
CIt becomes wider, because narrowing the slit increases the angular spread of diffraction
DIt disappears, because slits narrower than the wavelength produce no diffraction pattern
The width of the central maximum is inversely proportional to slit width: the first minimum occurs at sinθ = λ/a, so halving a doubles the angle to the first minimum — the central maximum doubles in width. This is the key inverse relationship: wider slits produce sharper, more compact diffraction patterns; narrower slits produce wider, more spread-out patterns. Option A is the common misconception — students expect a smaller opening to confine the light, but diffraction works opposite to geometric optics.
Question 2 Multiple Choice
Why does a single slit produce dark fringes? Which argument best explains the first minimum at asinθ = λ?
AThe slit absorbs light at the edges, creating periodic dark bands
BThe first minimum occurs when the path difference between the top and bottom of the slit equals exactly one full wavelength
CThe slit is divided into two halves; when each point in the top half cancels with the corresponding point in the bottom half (path difference λ/2), the entire slit destructively interferes
DThe dark fringes arise because single-slit diffraction and double-slit interference superpose and cancel at these angles
By pairing each point in the top half of the slit with a corresponding point half-a-slit-width below it, the path difference at the first minimum is (a/2)sinθ = λ/2 — causing destructive interference. Because EVERY pair across the entire slit cancels, the total amplitude at the screen is zero. The condition a sinθ = λ follows. The same pairing argument extends to higher minima by dividing the slit into 4, 6, 8 equal parts. Option B is wrong because it's the path difference between the top and midpoint (a/2) that equals λ/2, not the full slit width.
Question 3 True / False
A narrower slit produces a narrower diffraction pattern because less light passes through, reducing the spread.
TTrue
FFalse
Answer: False
This reverses the actual relationship. Narrowing the slit WIDENS the diffraction pattern — the central maximum grows broader and the secondary maxima spread out. This is captured by the inverse relationship in the minima condition: sinθ_min = λ/a. A smaller a means a larger θ for the first minimum, so the central maximum spans a wider angle. Geometric optics intuition (smaller hole = tighter beam) breaks down when the slit size approaches the wavelength; diffraction dominates and the pattern expands.
Question 4 True / False
The central maximum of a single-slit diffraction pattern is twice as wide (in angular terms) as each of the secondary maxima.
TTrue
FFalse
Answer: True
The central maximum spans from the first minimum on one side (θ = arcsin(λ/a)) to the first minimum on the other side — a total angular width of 2arcsin(λ/a), or approximately 2λ/a for small angles. The secondary maxima each span from one minimum to the next: from mλ/a to (m+1)λ/a — roughly λ/a wide. So the central maximum is indeed about twice the width of each secondary maximum. This asymmetry (wider central peak, progressively dimmer side bands) is the signature feature that distinguishes single-slit from double-slit patterns.
Question 5 Short Answer
Why does making a slit narrower cause the diffraction pattern to become wider rather than narrower?
Think about your answer, then reveal below.
Model answer: Single-slit diffraction arises from Huygens's principle: every point across the slit's width acts as an independent source of secondary wavelets, and these sources interfere with each other at the screen. Dark fringes appear where pairs of sources across the slit cancel destructively. The condition for the first dark fringe is asinθ = λ — where a is the slit width. A narrower slit (smaller a) requires a LARGER angle θ for this path difference to be reached, so the first dark fringe moves farther from center. The central maximum, bounded by the first dark fringes on either side, therefore becomes wider. The physical intuition is that a narrower aperture imposes a tighter spatial constraint, which by the wave uncertainty principle requires a broader angular spread.
This inverse relationship between aperture and diffraction spread is fundamental to optical instrument design: wide telescope mirrors give sharp images (narrow diffraction) but poor ability to resolve fine angular features near a bright source; narrow apertures give blurry images but reveal fine angular structure through wide diffraction.