Two parallel beams of light P and Q are incident normally on a prism and the transmitted rays are brought to focus with the help of a convergent lens as shown in Fig. 2.23. If the intensities of the upper and lower beams immediately after transmission from face AC are 4I and I, respectively, find the resultant intensity at the focus.

Answer

9I

Explanation

Path difference between rays 1 and 2:
`Deltax=mu(QS)-PR` …(i)
Further `(QS)/(PS)=sini,(PR)/(PS)=sinr`
`therefore(PR//PS)/(QS//PS)=(sinr)/(sini)=muthereforemu(QS)=PR`
Substituting in equation (i), we get `Deltax=0`
`therefore` Phase difference between rays 1 and 2 will be 0 or these two rays will interfere constructively. So maximum intensity will be obtained from their interference or
`I_(max)=(sqrt(I_(1))+sqrt(I_(2)))^(2)=(sqrt(4I)+sqrt(I))^(2)=9I`