Four light waves are represented by
(i) `y=a_1sin omegat`
(ii) `y=a_2 sin (omega t+varphi)`
(iii) `y=a_1sin 2 Omega t`
(iv) `y=a_2sin 2(omegat+varphi)`
Interference fringes may be observed due to superposition of

Options

A. (i) and (ii)
B. (i) and (iii)
C. (ii) and (iv)
D. (iii) and (iv)

Answer

A, D

Explanation

For interference to occur, the two sources should be coherent, i.e., their frequencies should be equal.
`:.` either `(omega)/(2pi)` or `(2 omega)/(2 pi)`. (i) and (ii) have same frequencies `(omega)/(2 pi)` and (iii) and (iv) also have same frequencies `(2 omega)/(2 pi)`.