Question

Write the conditions under which two light waves originating from two coherent sources can interfere each other (i) constructively, and (ii) destructively, in terms of wavelength. Can these be applied for two lights originating from two sodium lamps? Give reason.

Hint:

For interference to occur, the two light sources must be coherent, meaning they must emit light of the same frequency and phase. Sodium lamps emit incoherent light, so they cannot produce clear interference patterns.

Answer 1

The phenomenon of interference occurs when two coherent light waves meet, and their resultant amplitude is determined by the superposition principle. For two light waves originating from two coherent sources to interfere, the conditions for constructive and destructive interference are as follows: (i) Constructive Interference: For constructive interference to occur, the two light waves must meet in such a way that their amplitudes add up. This occurs when the path difference between the two waves is an integer multiple of the wavelength, i.e., \[ \Delta l = n \lambda \quad \text{where} \quad n = 0, 1, 2, 3, \dots \] where: - \( \Delta l \) is the path difference, - \( \lambda \) is the wavelength of the light, - \( n \) is any integer. (ii) Destructive Interference: For destructive interference to occur, the two light waves must meet in such a way that they cancel each other out. This occurs when the path difference between the two waves is an odd multiple of half the wavelength, i.e., \[ \Delta l = \left( n + \frac{1}{2} \right) \lambda \quad \text{where} \quad n = 0, 1, 2, 3, \dots \] where: - \( \Delta l \) is the path difference, - \( \lambda \) is the wavelength of the light, - \( n \) is any integer. Application to Two Sodium Lamps: For two sodium lamps, the light emitted is typically not coherent because the light from each lamp consists of multiple wavelengths (i.e., sodium lamps emit a broad spectrum of light, not a single wavelength). For interference to occur, the two sources must be coherent, meaning they must emit light of the same frequency and phase relationship. Since sodium lamps emit a mixture of different wavelengths, they are not suitable for creating interference patterns like those produced by coherent sources, such as lasers. Therefore, the conditions of constructive and destructive interference cannot be easily applied to the light from two sodium lamps. Conclusion: While the conditions for constructive and destructive interference are well-defined in terms of wavelength, they cannot be practically applied to the light from two sodium lamps because the light from sodium lamps is not coherent.