Question 185: Wave Optics

Question

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $x \mathrm{I}$. The value of $x$ is___________ .

Accepted Answer

Calculate Maximum Intensity ($I_{	ext{max}}$):
$    I_{\max} = \left(\sqrt{I_1} + \sqrt{I_2}ight)^2    $
Substituting the values, we have:
$    I_{\max} = \left(\sqrt{4I} + \sqrt{9I}ight)^2    $
$    I_{\max} = \left(2\sqrt{I} + 3\sqrt{I}ight)^2 = \left(5\sqrt{I}ight)^2 = 25I    $
Calculate Minimum Intensity ($I_{	ext{min}}$):
$    I_{\min} = \left(\sqrt{I_1} - \sqrt{I_2}ight)^2    $
Substituting the values, we have:
$    I_{\min} = \left(\sqrt{4I} - \sqrt{9I}ight)^2    $
$    I_{\min} = \left(2\sqrt{I} - 3\sqrt{I}ight)^2 = \left(-1\sqrt{I}ight)^2 = I    $
Calculate the Difference Between Maximum and Minimum Intensities:
$    I_{\max} - I_{\min} = 25I - I = 24I    $
Thus, the value of $x$, which represents the difference between the maximum and minimum intensities, is $24$.

Wave Optics

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is x \mathrm{I}. The value of x is___________ .

Integer / Numeric Answer Type