The two slits in Young’s double-slit experiment are illuminated by tw…

The correct answer is Option (3) → The two sources are incoherent. So, the interference pattern is not observed.

A steady interference pattern needs coherent sources, whose phase difference does not change with time.

Option (1) The wavelength, and hence the frequency, of the light is the same from both sources. So, interference is observed. — Incorrect. Equal wavelength is not enough. The phase difference between the two lamps changes randomly, so the bright and dark positions shift far too fast to be seen.

Option (2) The two sources act as coherent sources. So, interference is observed. — Incorrect. Two independent lamps have no fixed phase relationship, so they are not coherent. Young made his slits coherent by lighting both from one source.

Option (3) The two sources are incoherent. So, the interference pattern is not observed. — Correct. Light from an ordinary source such as a sodium lamp undergoes abrupt phase changes in about \( 10^{-10}\,\mathrm{s} \). The two lamps are therefore incoherent, the intensities just add up on the screen, and no fringes appear.

Option (4) Instead of interference, a diffraction pattern is observed. — Incorrect. Using two separate lamps does not turn the experiment into a diffraction set-up. The screen shows only the sum of the two intensities, which is a uniform illumination.

NCERT (2026-27):
Interference of Light Waves and Young’s Experiment – “We will now discuss interference using light waves. If we use two sodium lamps illuminating two pinholes … we will not observe any interference fringes. This is because of the fact that the light wave emitted from an ordinary source (like a sodium lamp) undergoes abrupt phase changes in times of the order of 10^–10 seconds. Thus the light waves coming out from two independent sources of light will not have any fixed phase relationship and would be incoherent, when this happens, as discussed in the previous section, the intensities on the screen will add up.”