Q4. Assertion: two independent sodium lamps placed side by side give no interference fringes. Reason: their light has different wavelengths. Are both true, and does the reason explain the assertion?
The assertion is true but the reason is false: the two lamps give the same sodium light, but each changes its phase abruptly and independently about every 10−10 s, so they are incoherent (NCERT page 265).
Q5. At a point the resultant intensity from two equal coherent sources is 3I0. What is the smallest phase difference there?
4I0 cos2(φ/2) = 3I0 gives cos(φ/2) = √3/2, so φ/2 = π/6 and φ = π/3 (NCERT Eq. (10.11), page 264).
Q6. The amplitudes of two coherent waves are in the ratio 2 : 1. Find Imax/Imin.
(2 + 1)2/(2 − 1)2 = 9 (beyond the NCERT text; intensity goes as amplitude squared, NCERT page 263).
Q7. Show that the average of 4I0 cos2(φ/2) over a whole cycle of φ is 2I0, and say what this means.
4I0 cos2(φ/2) = 2I0(1 + cos φ), and cos φ averages to zero over a cycle, leaving 2I0. Interference only moves energy from dark places to bright ones; the total is the same as without interference (NCERT Eq. (10.12), page 264, and page 268).