Question 70: Wave Optics

Question

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Accepted Answer

To find the ratio of the intensities of the maximum to the minimum in an interference pattern formed by two monochromatic light beams with intensity ratios of 1:9, you use the formula:
$ \frac{I_{\max }}{I_{\min }} = \frac{\left(\sqrt{I_1} + \sqrt{I_2}\right)^2}{\left(\sqrt{I_1} - \sqrt{I_2}\right)^2} $
Given that the intensity ratio is 1:9, we have $I_1 = 1$ and $I_2 = 9$.
Calculate $\sqrt{I_1}$ and $\sqrt{I_2}$:
$   \sqrt{I_1} = \sqrt{1} = 1   $
$   \sqrt{I_2} = \sqrt{9} = 3   $
Substitute these values into the formula:
$   \frac{I_{\max }}{I_{\min }} = \frac{(1 + 3)^2}{(1 - 3)^2} = \frac{4^2}{2^2} = \frac{16}{4} = 4   $
Thus, the ratio of the intensities of the maximum to the minimum is 4:1.

Answer

$8: 1$

Answer

$4: 1$

Answer

$3: 1$

Answer

$9: 1$

Wave Optics

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

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