In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on `theta` for constructive interference at P between the ray BP and reflected ray OP.

Options

A. `costheta=3lamda//2d`
B. `costheta=lamda//4d`
C. `sectheta-costheta=lamda//d`
D. `sectheta-costheta=4lamda//d`

Answer

B

Explanation

`PO=dsecthetaandCO=POcos2theta=dsecthetacos2theta`
Path difference,
`Deltax=CO+PO`
= `(dsectheta+dsecthetacos2theta)`
Effective path difference
`Deltax_(eff)=d(sectheta+sectheta*cos2theta)+lamda/2`
For constructive interference,
`Deltax_(eff)=lamda`
or `d(sectheta+secthetacos2theta)+lamda/2=lamdaorcostheta=lamda/(4d)`.