A narrow tube is bent in the form of a circle of radius R, as shown in figure. Two small holes S and D are made in the tube at the position at right angle to each other. A source placed at S generates a wave of intensity `I_(0)` which two parts: one part travels along the longer path, while the other travels along the shorter path. Both the waves meet at point D where a detector is placed.

1. If a maxima if formed at a detector, then the magnitude of wavelength `lambda` of the, wave produced is given by

Options

A. `pi` R
B. `pi` R/(2)
C. `pi` R/(4)
D. all of these

Answer

d

Explanation

Path difference produced is `Delta x = (3)/(2) pi R - (pi)/(2) R = pi R`
For maxima: `Delta x = n lambda`
`:.n lambda = pi R`
`implies lambda =(pi R)/(n) , n = 1, 2, 3`,…
Thus, the possible values of `lambda` are `pi R ,(pi R)/(2),(pi R)/(3)`