Question

Two coherent monochromatic light beams of intensities $I$ and $9I$ are super imposed. The maximum and the minimum intensities of the resultant beam are

• A. $10I$ and zero
• B. $10I$ and $8I$
• C. $10I$ and $4I$
• D. $16I$ and $4I$

Answer 1

The correct option is D $16I$ and $4I$

The resultant intensity , $I_R=I_1+I_2+2\sqrt{I_1{I}_2}cos\delta$

where $\delta$ be the phase difference between the two waves.

For maximum intensity, $\delta =0^o$ so $I_{R_{max}}=I+9I+2\sqrt{I\left(9I\right)}cos0=16I$

For minimum intensity, $\delta ={180}^o$ so $I_{R_{min}}=I+9I+2\sqrt{I\left(9I\right)}cos180=4I$