The arrangement for a mirror experiment is shown in figure. S is a point source of frequency `6xx10^(14)Hz`. D and C represent the two ends of a mirror placed horizontally and LOM represents the screen.

Determine the width of the region where the fringes will be visible

Options

A. 4cm
B. 6cm
C. 2cm
D. 3cm

Answer

C

Explanation

Fringes will be observed in the region between `P_(1)` and `P_(2)` because the reflected rays lie only in this region. From similar triangles : `BDS_(1) asnd S_(1)P_(2)A` .
`(AP_(2))/(BS_(1)) = (AS_(1))/(BD) , BS_(1) = BS = 1mm = 10^(-1) cm`
`AP_(2) = (AS_(1)xxBS_(1))/(BD) = (200xx0.1)/(5) = 4cm AP_(2) = 4cm`
Similarly, `BCS_(1)` and `S_(1)P_(1)A` are similar triangles
`(AP_(1))/(BS_(1)) = (AS_(1))/(BD) AP_(1) = (AS_(1)xxBS_(1))/(BD) = (200xx0.1)/(10) = 2cm`
Width of the region where fringes observed is
`P_(1)P_(2) = AP_(2) - AP_(2) = 4-2 = 2cm , P_(1)P_(2) = 2 cm`