Question

The intensity of two waves is $2$ and $3$ unit, then average intensity of light in the overlapping region will have the value:

• A. $2.5$
• B. $6$
• C. $5$
• D. $13$

Answer 1

The correct option is C $5$

Given,

$I_1=2unit$

$I_2=3unit$

We know that,

$I_{max}=I_1+I_2+2\sqrt{I_1{I}_2}$. . . . . . . .(1)

$I_{max}=2+3+2\sqrt{2\times 3}=5+2\sqrt{6}unit$

$I_{min}=I_1+I_2-2\sqrt{I_1{I}_2}$. . . . . . .. . . .(2)

$I_{min}=2+3-2\sqrt{2\times 3}=5-2\sqrt{6}unit$

The average intensity,

$I_a=\frac{I_{max}+I_{min}}{2}$

$I_a=\frac{5+2\sqrt{6}+5-2\sqrt{6}}{2}=5unit$

The correct option is C.