If a point P of a continuous and elastic medium is hit by two waves Ψ1 and Ψ2, emitted by two different sources O1 and O2, from which it has distances, respectively, r1 and r2, it oscillates as if it were hit by a single wave Ψ resulting from the sum of Ψ1 and Ψ2.

Interference of light

If we project a beam of polarized monochromatic light on an opaque diaphragm, in which were made two thin straight slits, parallel to each other and perpendicular to the plane of polarization of the light and behind the diaphragm we put a white screen, at a distance large enough so we can consider this distance infinite with respect to the distance d between the slits, we observe on the screen not just two bright stripes corresponding to the slots, as one would expect based on the principles of geometrical optics, but a series, which could be very large, of bright stripes separated by dark stripes.

These strips are called interference fringes and they can be explained, only admitting that the light is a wave. In fact, on the basis of experiences of this kind, made by T. Young, the physicists of the nineteenth century, rejected the hypothesis, supported by Newton, that light is made up of small discrete particles.


By accepting the Huygens' principle, we interpret the slits A and B of the figure, reached at the same time by the same wavefront, as sources of elementary cylindrical waves, which interfere in the point P of the screen OP, having distances r1 from A and r2 from B.

If O is the point of the screen on the geometrical axis CO of the segment AB, and we denote by d the length of the segment AB and by α the angle OCP and assume that the distance CO is infinite with respect to d, we have


From the equation (5.2) we have


The maximum of the amplitude Amax is reached when α=0 and is 2A, so


The intensity, which is visually perceived as light intensity, from the equation (3.26), is proportional to the square of the amplitude, thus


The intensity of the strip has its maximum when the absolute value of the cosine is 1, ie if


From the equation (5.6) we can see that our calculations make sense only if λ<d. Moreover, if nmax is the maximum value of n,


then in the equation (5.6) n takes integer values from -nmax to nmax so will see 2n-1 bright fringes separated by dark fringes. In the example shown in the graph below we assume λ = 1/4 d.


If we represent by φ the phase shift between the two waves emitted by A and B in a point on the screen


the equation (5.5) can be rewritten as


The equation (5.9) expresses in general the intensity due to interference of waves of equal amplitude and angular frequency and with a mutual phase shift φ.