Physics · Wave Optics · NEET
No. Path difference (usually written as delta or x) is a real distance, measured in metres, centimetres, or in units of wavelength lambda. Phase difference (phi) is an angle, measured in radians (or degrees), that tells how far apart two waves are inside one cycle. They describe the same lag but in different languages: one in length, one in angle. The bridge between them is phi = (2 pi / lambda) x path difference.
Use phi = (2 pi / lambda) x (path difference). Steps: (1) make sure path difference and lambda are in the same unit (both in metres, or both in nm). (2) Divide path difference by lambda to get how many wavelengths it is. (3) Multiply by 2 pi. Example: if path difference = lambda/4, then phi = (2 pi / lambda)(lambda/4) = pi/2 radians = 90 degrees.
The quantity 2 pi / lambda is called the wave number, written as k. It says how much phase (in radians) the wave gains per unit of distance travelled. Over a distance of one full wavelength lambda, the wave gains exactly 2 pi radians, which is one complete circle. So multiplying the path difference by k = 2 pi / lambda simply converts a length into an angle.
A wave repeats itself after every one wavelength. So if one wave travels an extra distance of exactly lambda, it comes back to the same point in its cycle as the other wave. Being back to the same point means it is a full circle ahead, which is 2 pi radians (360 degrees). Both waves then line up crest-to-crest, giving constructive interference.
Set phi = pi in phi = (2 pi / lambda) x delta. Solving: delta = lambda/2. So a path difference of half a wavelength gives a phase difference of pi (180 degrees). Here a crest of one wave meets a trough of the other, and they cancel: this is destructive interference. In general, path difference (n + 1/2) lambda gives phase (2n + 1) pi.
Path difference has a length unit (metre, cm, nm, or expressed as a multiple of lambda). Phase difference has no length unit; it is an angle in radians or degrees. Radian is dimensionless, so phase difference is often written as a plain number times pi. Mixing them up (writing phase in metres or path in radians) is a common mistake in NEET options.
The intensity at the maximum in a Young's double slit experiment is I0. Distance between two slits is d = 5 lambda, where lambda is the wavelength of light used. What will be the intensity in front of one of the slits on the screen placed at a distance D = 10d?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Phase difference phi = (2 pi / lambda) x path difference. Rearranged, path difference = (lambda / 2 pi) x phi. Here lambda is the wavelength.
phi = (2 pi / lambda)(lambda/2) = pi radians, which is 180 degrees. This is the destructive interference condition.
k = 2 pi / lambda. It is the phase gained per unit distance and is the conversion factor from path difference to phase difference.
No. Path difference is a length. To express the lag as an angle you must convert it to phase difference using phi = (2 pi / lambda) x path difference.
Path difference = n lambda (n = 0, 1, 2, ...) and phase difference = 2 n pi. Both mean the waves are perfectly in step.
