Question

Two sources of intensity $2I$ and $8I$ are used in an interference experiment. The intensity at a point where the waves from two sources superimpose with a phase difference of :
(a) zero
(b) $\pi /2$
(c) $\pi$

• A. $18I,10I,2I$
• B. $5I,4I,I$
• C. $2I,I,\frac{I}{2}$
• D. $2I,10I,18I$

Answer 1

The correct option is A $18I,10I,2I$

Intensity after interference is given by
a ) zero

$I_f=I_1+I_2+2\sqrt{I_1{I}_2}\cos \theta$
$=2I+8I+2\times 4I\times \cos \theta$
$=18I$

b) $\pi /2$

$I_f=I_1+I_2+2\sqrt{I_1{I}_2}\cos \theta$
$=2I+8I$
$=10I$

c) $\pi$

$I_f=I_1+I_2+2\sqrt{I_1{I}_2}\cos \theta$
$=2I+8I-8I$
$=2I$