Physics · Waves · NEET
Both come from adding two overlapping waves (superposition). Constructive interference happens when the two waves are IN PHASE — a crest lands on a crest. The displacements add, so the resultant amplitude is a1 + a2 (maximum), giving a bright fringe (light) or a loud point (sound). Destructive interference happens when they are OUT OF PHASE by half a cycle — a crest lands on a trough. The displacements subtract, so the amplitude is |a1 - a2|. If the two amplitudes are equal, the result is ZERO everywhere at that point — a dark fringe or silence.
Use path difference (extra distance one wave travels) Dx or phase difference phi. Constructive: path difference = n*lambda (0, lambda, 2*lambda, ...), or phase difference phi = 2*n*pi. The waves meet in step. Destructive: path difference = (n + 1/2)*lambda (lambda/2, 3*lambda/2, ...), or phase difference phi = (2n+1)*pi. The waves meet exactly opposite. Here n = 0, 1, 2, 3... Remember: whole wavelengths add, half wavelengths cancel.
Path difference Dx is the extra distance the wave from one source travels compared to the other to reach a point. Phase difference phi is how much the two waves are 'shifted' in their cycle, measured in radians. They are linked by: phi = (2*pi / lambda) * Dx So one full wavelength of path difference (Dx = lambda) equals a phase difference of 2*pi (a full cycle). Half a wavelength (Dx = lambda/2) equals a phase difference of pi (opposite).
No. Energy is never destroyed, it is only REDISTRIBUTED. At a dark/silent point the energy is missing, but at the neighbouring bright/loud points the intensity is EXTRA (up to 4 times one source's intensity, since I = 4*I0*cos^2(phi/2)). Averaged over the whole pattern, total energy is conserved. NCERT and NEET both stress this: interference obeys conservation of energy.
Coherent sources keep a CONSTANT phase difference over time (and same frequency). Then the bright and dark points stay fixed, so you SEE a steady pattern. Two independent bulbs are incoherent — their phase difference jumps randomly (every ~10^-10 s), so bright and dark keep swapping too fast to see, and the intensities just add up with no visible fringes. This is why Young used one source split into two slits.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Phase difference phi = 0, 2*pi, 4*pi, ... i.e. phi = 2*n*pi (an even multiple of pi). The waves are exactly in step and amplitudes add.
Constructive: resultant amplitude = a + a = 2a, and intensity = 4*I0. Destructive: resultant amplitude = a - a = 0, and intensity = 0 (for equal amplitudes).
I = 4*I0*cos^2(phi/2), where I0 is the intensity of one source and phi is the phase difference. Maximum (4*I0) when phi = 0, minimum (0) when phi = pi.
Superposition is the general rule: the net displacement is the algebraic sum of the individual displacements. Interference is the specific PATTERN of bright/loud (constructive) and dark/quiet (destructive) points that results when two coherent waves superpose.
All waves interfere — sound, water, light and even matter waves. NCERT uses two needles in a water trough and two loudspeakers as examples. Interference is not special to light.
