Question

The slits in a Young's double- slit experiment have equal width and the source is placed symmetrically with respect to the slits. The intensity at the central fringe is $I_o$. If one of the slit is closed, the intensity at this point will be_______

• A. $I_o$
• B. $\frac{I_o}{4}$
• C. $\frac{I_o}{2}$
• D. $4I_o$

Answer 1

The correct option is B $\frac{I_o}{4}$

for interference of two waves,
$I_{total}=I_1+I_2+2\sqrt{I_1{I}_2}\cos \theta$
for equal intensities and central fringe,
$I_{total}={4I}_1=I_0$ ..... given.
$\therefore I_1=\frac{I_0}{4}$
Hence when one slit is closed the intensity will be $\frac{I_0}{4}$