L.: la veraldn que conjugando las concepoionee saussurlanas chomskyanas y referenclallstas con el modelo clentiflco a^
2.3.3. Critica a la concepcidn del lenguaje como cdl- culo con oraciones elementales y/o nombres
Interference for light was fi rst demonstrated in 1801 by Thomas Young.
Figure 4.57 shows plane wavefronts of light approaching two extremely thin, parallel, vertical slits. Because of diff raction the wavefronts spread out from each slit. Wavefronts from the slits arrive on a screen and so interfere.
At those points on the screen where the path diff erence is an integral multiple of the wavelength of light constructive interference takes place.
The screen looks bright at those points, marked on the diagram as n = 0, n = ±1, … . The value of n indicates that the path diff erence is nλ. At other points where the path diff erence is a half-integral multiple of λ, the screen looks dark: we have destructive interference.
λ
n = 4 n = 3 n = 2
n = –2 n = –3 n = –4 n = 1
n = –1 n = 0 central
maximum top view of double slit
d
D
S
y/cm
The distance on the screen between the middle of a bright spot and the middle of the next bright spot is called the ‘fringe spacing’ and is denoted by s. It can be shown that:
s = λD d
where D is the distance between the slits and the screen and d is the distance between the slits.
The graphs in Figure 4.58 show how the intensity of the waves on the screen varies with distance from the middle of the screen. The graph in Figure 4.58a applies if the slit width is negligible. In this case successive peaks in intensity (corresponding to points of constructive interference) have the same intensity and are separated by a distance equal to s. The graph in Figure 4.58b shows the intensity when the slit width cannot be neglected. In this case the width is about 45 times the wavelength.
In Figure 4.58, the units on the vertical axis are arbitrary. An intensity of one unit corresponds to the intensity from only one slit. At points of constructive interference the amplitude is double that of just one wave.
Since intensity is proportional to the square of the amplitude, the intensity is four times as large. Figure 4.59 shows actual interference patterns with two slits and two diff erent wavelengths.
Worked example
4.15 Use the graph in Figure 4.58a for this question. In a double-slit interference experiment the two slits are separated by a distance of 4.2 × 10−4 m and the screen is 3.8 m from the slits.
a Determine the wavelength of light used in this experiment.
b Suggest the eff ect on the separation of the fringes of decreasing the wavelength of light.
c State the feature of the graph that enables you to deduce that the slit width is negligible.
a Reading from the graph, the separation of the bright fringes is 0.50 cm. Applying s = λD
b From the separation formula we see that if we decrease the wavelength the separation decreases.
c The intensity of the side fringes is equal to the intensity of the central fringe.
Figure 4.58 The intensity pattern for two slits a of negligible width and b with a slit width that is not negligible. The horizontal axis label y refers to the distance from the centre of the screen.
Figure 4.59 Slit patterns for two slits of fi nite width with two diff erent wavelengths. Notice that the largest separation of the fringes is obtained with the longest wavelength i.e.
red light.
Exam tip Watch the units!
Nature of science
Competing theories and progress in science
At the start of this section we mentioned the confl ict between the Newton and Huygens over the nature of light. In 1817 Augustin-Jean Fresnel published a new wave theory of light. The mathematician Siméon Poisson favoured the particle theory of light, and worked out that Fresnel’s theory predicted the presence of a bright spot in the shadow of a circular object, which he believed was impossible. François Arago, a supporter of Fresnel, was able to show there was indeed a bright spot in the centre of the shadow. In further support of his theory, Fresnel was able to show that the polarisation of light could only be explained if light was a transverse wave. The wave theory then took precedence, until new evidence showed that light could behave as both a wave and a particle.
28 The speed of sound in air is 340 m s−1 and in water it is 1500 m s−1. Determine the angle at which a beam of sound waves must hit the air–
water boundary so that no sound is transmitted into the water.
29 Planar waves of wavelength 1.0 cm approach an aperture whose opening is also 1.0 cm. Draw the wavefronts of this wave as they emerge through the aperture.
30 Repeat question 52 for waves of wavelength 1 mm approaching an aperture of size 20 cm.
31 A radio station, R, emits radio waves of wavelength 1600 m which reach a house, H, directly and after refl ecting from a mountain, M, behind the house (see diagram). The reception at the house is very poor. Estimate the shortest possible distance between the house and the mountain. (Pay attention to phase changes.)
Test yourself
enters glass with a refractive index of 1.583, with an angle of incidence of 38°. Calculate:a the angle of refraction b the speed of light in the glass c the wavelength of light in the glass.
26 Light of frequency 6.0 × 1014 Hz is emitted from point A and is directed toward point B a distance of 3.0 m away.
a Determine how long will it take light to get to B.
b Calculate how many waves fi t in the space between A and B.
27 A ray of light is incident on a rectangular block of glass of refractive index 1.450 at an angle of 40°, as shown in the diagram. The thickness of the block is 4.00 cm. Calculate the amount d by which the ray is deviated.
4.5 Standing waves
A special wave is formed when two identical waves travelling in opposite directions meet and interfere. The result is a standing (or stationary) wave:
a wave in which the crests stay in the same place. The theory of wind and string musical instruments is based on the theory of standing waves.