Wave Optics

The correct answer is (D) :460 cm^-1

Concept: Phase velocity is the velocity with which a single wave phase propagates through space. where

• = angular frequency
• = wave number

Step 1: Define group velocity.} Group velocity is the velocity at which the envelope of a wave packet (or energy) travels.
Step 2: Condition for a non-dispersive medium.} In a non-dispersive medium, the wave speed does not depend on frequency. This means
Step 3: Resulting relationship.} Under this condition, Thus, in a non-dispersive medium, the group velocity equals the phase velocity.

Concept: Polarization is a phenomenon in which the vibrations of a wave are restricted to a particular direction.
Step 1: Understand wave behavior.} Only transverse waves can exhibit polarization because their oscillations occur perpendicular to the direction of propagation.
Step 2: Implication for electromagnetic waves.} When light waves are polarized, it proves that their electric field oscillates in directions perpendicular to the direction of propagation.
Step 3: Conclusion.} Thus, the phenomenon that confirms the transverse nature of electromagnetic waves is polarization.

Concept: In Young’s Double Slit Experiment (YDSE), the fringe width is given by where

• = wavelength of light
• = distance between the screen and slits
• = separation between the slits

Step 1: Effect of medium on wavelength.} When light enters a medium like water with refractive index , its wavelength changes according to
Step 2: Substitute new wavelength in fringe width formula.}
Step 3: Compare fringe widths.} Since for water, the fringe width becomes smaller. Thus, the fringe width decreases.