Two monochromatic light beams of intensity 16 and 9 units are...

Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is:

Options

A $\frac{16}{9}$
B $\frac{4}{3}$
C $\frac{7}{1}$
D $\frac{49}{1}$

Correct answer

D. $\frac{49}{1}$

Step-by-step solution

Intensity

\propto(\text{ amplitude })^2

\begin{aligned}&\frac{I_1}{I_2}=\frac{16}{9}=\frac{a_1^2}{a_2^2}\\ &\Rightarrow \mathrm{a}_{1}=4 ; \mathrm{a}_{2}=3 \end{aligned}

Therefore

the ratio of intensities of bright and dark parts\frac{I_{\text{Bright }}}{I_{\text{Dark }}}=\frac{\left(a_1+a_2\right)^2}{\left(a_1-a_2\right)^2}=\frac{(4+3)^2}{(4-3)^2}=\frac{49}{1}

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