Questions on diffraction and the single slit

Question 1

Describe what is meant by diffraction, and state when the spreading of a wave at a gap is greatest.

Accepted Answer

Diffraction is the spreading of a wave as it passes through a gap or around an obstacle (1). The spreading is greatest when the gap width is about the same size as the wavelength (1).

Question 2

Sketch the intensity pattern produced when monochromatic light passes through a single narrow slit, and describe its main features.

Accepted Answer

A bright central maximum with much dimmer maxima either side (1). The central fringe is twice as wide as the others and far brighter; the outer fringes decrease in brightness with distance from the centre (1).

Question 3

State what happens to the single-slit diffraction pattern when the slit is made narrower.

Accepted Answer

The fringes spread out (1): the central maximum (and all the fringes) become wider (1).

Question 4

Sea waves of wavelength 12 m pass through a harbour entrance 15 m wide. State and explain how the waves behave beyond the entrance.

Accepted Answer

The entrance is about the same size as the wavelength (1), so the waves diffract strongly, spreading into the harbour as near-circular wavefronts (1).

Question 5

State two ways in which the appearance of a single-slit diffraction pattern differs from the double-slit fringe pattern produced with the same light.

Accepted Answer

In the single-slit pattern the central maximum is twice the width of the other maxima, whereas double-slit fringes are all the same width and evenly spaced (1). In the single-slit pattern the side maxima are much dimmer than the centre, whereas double-slit fringes are (nearly) equally bright (1).

Question 6

Explain why sound is clearly diffracted through an open doorway but light passing through the same doorway is not noticeably diffracted.

Accepted Answer

Diffraction is significant when the gap is comparable to the wavelength (1). Sound wavelengths are of the order of the door width (about a metre), so sound diffracts strongly (1); the wavelength of light is around 10⁻⁷ m, far smaller than the doorway, so its diffraction is negligible (1).

Question 7

Describe how the single-slit diffraction pattern changes when the light is switched from blue to red, for the same slit.

Accepted Answer

Red light has a longer wavelength than blue (1), so it diffracts more (1). The fringes, including the central maximum, become wider and more spread out for red than for blue (1).

Question 8

Describe the single-slit diffraction pattern produced with white light.

Accepted Answer

The central maximum is white (all wavelengths overlap there) (1). The side maxima are spread into colours, with blue/violet closest to the centre and red furthest out, because longer wavelengths diffract more (1); the fringes overlap and become less distinct further out (1).

Question 9

Explain why the central maximum of a single-slit pattern is both wider and brighter than the other fringes.

Accepted Answer

Most of the light energy passes near the straight-through direction, giving the central fringe its high intensity (1). It spans the region between the first minima on either side (1), which is twice the spacing of the outer fringes, so it is also twice as wide (1).

Question 10

A student illuminates an adjustable slit with a red laser and slowly narrows the slit, starting from a width of several millimetres. Describe how the pattern on a distant screen changes as the slit narrows.

Accepted Answer

At first the slit is far wider than the wavelength, so the screen shows a narrow strip of light with very little spreading (1). As the slit narrows the light spreads out more and a diffraction pattern appears: the central maximum and the side fringes become wider (1). The pattern also becomes dimmer, because a narrower slit lets less light through (1).

Question 11

Microwaves of wavelength 2.8 cm pass through a vertical gap between two metal plates whose separation can be adjusted. State the approximate gap width that gives the greatest spreading of the microwaves, and describe and explain what a detector moved across the region beyond the gap records when the gap is 50 cm wide.

Accepted Answer

Greatest spreading when the gap is about 3 cm, comparable to the wavelength (1). A 50 cm gap is many times the wavelength, so there is little diffraction (1); the detector records a strong signal only in the straight-through region directly beyond the gap, falling off sharply at its edges (1).

Question 12

In a single-slit experiment, the slit width and the wavelength of the light are both doubled. Explain what happens to the width of the central maximum.

Accepted Answer

The amount of spreading depends on how the wavelength compares with the gap width, the ratio of wavelength to slit width (1). Doubling both leaves that comparison unchanged (1), so the width of the central maximum is (almost) unchanged (1).

Question 13

State Huygens' construction, and use it to explain why a plane wavefront travelling across open water stays plane.

Accepted Answer

Every point on a wavefront acts as a source of a secondary wavelet, a small circular wave spreading forwards at the wave speed (1). After a short time every wavelet has grown to the same radius, and the new wavefront is the envelope of the wavelets, the surface that just touches all of them (1). In open water the wavelet centres lie along a straight line and every wavelet has the same radius, so their common tangent is another straight line one radius further on; each wavelet's sideways bulge is buried inside its neighbours' circles and never reaches the envelope, so the wavefront stays plane (1).

Question 14

Two single slits of different widths are each illuminated with the same monochromatic light. Explain which slit produces the wider central maximum, and what happens to the brightness.

Accepted Answer

The narrower slit produces the wider central maximum (1), because narrower gaps diffract more (1). However, a narrower slit lets less light through (1), so although its pattern is more spread out, the overall pattern is dimmer than that from the wider slit (1).

Question 15

Explain why a laser is well suited to demonstrating diffraction patterns.

Accepted Answer

Laser light is monochromatic (single wavelength) and coherent (1), so the diffracted waves keep a constant phase relationship and the same fringe positions (1). This gives a sharp, well-defined pattern of a single colour rather than a blurred, overlapping one (1).

Question 16

A teacher wants to project the widest possible single-slit central maximum. Three arrangements are available.
Arrangement W: laser of wavelength 650 nm, slit width 0.10 mm.
Arrangement X: laser of wavelength 532 nm, slit width 0.10 mm.
Arrangement Y: laser of wavelength 650 nm, slit width 0.20 mm.
Deduce which arrangement the teacher should choose.

Accepted Answer

Spreading is greater when the wavelength is a larger fraction of the slit width (1). W beats X because, for the same slit, the longer wavelength diffracts more; W beats Y because, for the same wavelength, the narrower slit diffracts more (1). So arrangement W gives the widest central maximum and should be chosen (1).

Question 17

A single slit is illuminated with white light. A student then places a red filter between the lamp and the slit. Describe and explain how the pattern on the screen changes.

Accepted Answer

The filter transmits only the long-wavelength red light, so the whole pattern, including the central maximum, becomes red and dimmer (1). Each side maximum becomes a single red fringe instead of a spectrum (1), centred where the red (outer) edge of the coloured fringe was, because red diffracts most (1). Only one wavelength now forms the pattern, so the minima are properly dark and the fringes stay distinct further from the centre (1).

Question 18

Water waves in a ripple tank meet a barrier with a gap in it, and then a second barrier consisting of a single small obstacle. Use Huygens' construction to explain how the waves reach the region behind each barrier, and why the spreading at the gap increases as the gap is narrowed.

Accepted Answer

A barrier deletes every wavelet source it covers, leaving only the wavelets in the gap (1). Across the middle of the gap the surviving wavelets still have neighbours on both sides, so the envelope there is still flat (1). At each edge the last surviving wavelet has no neighbour beyond it, so nothing buries its outer flank and the envelope wraps round it into the region straight-line travel would have left dark; that wrapping is the diffraction (1). At the obstacle the deletion is in the middle instead, so the wavelets at the two exposed edges have nothing inside them to bury their inner flanks and each curls into the shadow behind it (1). Narrowing the gap leaves fewer wavelets with neighbours, and once the gap is down to about one wavelength hardly more than a single wavelet survives; a single wavelet is a circle, so the wave leaves the gap spreading into every forward direction (1).