Question: Two sources of light are said to be coherent, when both emit light waves of:

Step 1 (Definition & Governing Principle): [0.5 Mark]

According to the NCERT Physics textbook (Wave Optics), two sources of light are defined as coherent if they emit light waves that maintain a stable interference pattern over time. The fundamental conditions for coherence are:

• The waves must have the same frequency (and therefore the same wavelength, $\lambda$).
• The phase difference ($\phi$) between the waves must remain constant with respect to time, i.e., $\frac{d\phi}{dt} = 0$.

Step 2 (Analysis of Options): [0.25 Mark]

• (i) Incorrect: Varying phase difference leads to an unstable interference pattern.
• (ii) Correct: Matches the definition of same wavelength ($\lambda_1 = \lambda_2$) and constant phase difference ($\Delta\phi = \text{constant}$).
• (iii) Incorrect: Different wavelengths result in different frequencies, preventing a stable interference pattern.
• (iv) Incorrect: Different wavelengths prevent the formation of a stable interference pattern.

Step 3 (Final Concluded Answer): [0.25 Mark]

The correct option is (ii) same wavelength and a constant phase difference.

💡 EL10 Concept Insight: Imagine two people jumping rope in perfect sync; because they move at the same speed and keep the same distance between them at all times, their pattern stays steady. Coherent light sources are just like that—they "jump" at the same frequency and stay in perfect step with each other so their waves can overlap to create a clear, steady pattern.