Find the value of `theta` for which a maxima is obtained at P.

Explanation

For maxima at P, `Delta x = lambda`
Path difference between direct & reflected ray
`= d sec theta cos 2 theta + (lambda)/(2)+d sec theta = lambda`
`d sec theta (1+cos 2theta)=(lambda)/(2)`
`d sec theta (2 cos^(2)theta)=(lambda)/(2)`
`cos theta = (lambda)/(4 d)`
`rArr theta = cos^(-1)((lambda)/(4d))`