How to solve Assertion-Reason questions:

1. Check if A is true
2. Check if R is true independently
3. If both true: check if R correctly explains A (option A vs B)
4. If one false: use options C or D

Key A/R pairs for Wave Optics:

Pair 1:

• A: Two independent sodium lamps don't produce sustained interference.
• R: Coherent sources need constant phase difference.
• Answer: A — Both true; R explains A. ✓

Pair 2:

• A: In YDSE with white light, the central fringe is white.
• R: At center, path difference = 0 for all wavelengths → all constructively interfere.
• Answer: A — Both true; R explains A. ✓

Pair 3:

• A: Single slit central maximum is twice as wide as secondary maxima.
• R: First minimum of central max is at $\sin\theta = \lambda/a$; secondary maxima are between consecutive minima.
• Answer: A — Both true; R explains A. ✓

Pair 4:

• A: At Brewster's angle, reflected beam is completely polarized.
• R: Reflected and refracted rays are perpendicular at Brewster's angle.
• Answer: A — Both true; R is correct explanation (this geometry forces complete polarization). ✓

Pair 5:

• A: Polarization proves light is a transverse wave.
• R: Only transverse waves can be plane-polarized.
• Answer: A — Both true; R explains A. ✓

Pair 6:

• A: Inserting a third polaroid between two crossed polaroids allows some light through.
• R: The middle polaroid rotates the plane of polarization, so some light passes the final polaroid.
• Answer: A — Both true; R explains A. ✓

Pair 7:

• A: In YDSE, fringe width decreases when apparatus is immersed in denser medium.
• R: Wavelength of light decreases in denser medium.
• Answer: A — Both true; R explains A (since $\beta = \lambda D/d$ and $\lambda$ decreases). ✓