The maximum intensity of fringes in Young's experiment is I. If one of the slit is closed, then the intensity at that place becomes `I_o`. Which of the following relation is true?

Options

A. `I=I_(0)`
B. `I=2I_(0)`
C. `I=4I_(0)`
D. `I=0`

Answer

C

Explanation

Consider the slit widths to be equal, so that they produces waves of equal intensity say, I' . Resultant intensity at any point `I_(R)=4I'cos^(2)phi`, where `phi` is the phase difference betweeen the wave ata the point observation.
For maximum intensity, `phi=0^(@) rArr I_("max")=4I'=I " "`...(i)
If, one of slit is closed, resultant intensity at the same point will be I' only, i.e.
`I'=I_(0)" "`(ii)
Comparing Eqs. (i) and (ii), we get `I=4I_(0)` .