Wave Optics

JEE Main level, single correct, medium

17 of 191

Question 17 of 191

Two coherent light sources having intensity in the ratio 2x2x produce an interference pattern. The ratio Imax⁡−Imin⁡Imax⁡+Imin⁡\dfrac{{I}_{\max }-{I}_{\min }}{{I}_{\max }+{I}_{\min }} will be

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Answer: (C) 22x2x+1\dfrac{2\sqrt{2x}}{2x+1}

Given that, I1I2=2x\dfrac{{I}_{1}}{{I}_{2}}=2x.
We know,
{I}_{\max }={\left(\sqrt{{I}_{1}}+\sqrt{{I}_{2}}\right)}^{2}&{I}_{\min }={\left(\sqrt{{I}_{1}}-\sqrt{{I}_{2}}\right)}^{2}
∴Imax⁡−Imin⁡Imax⁡+Imin⁡=2I1I2I1+I2=2I1/I2I1I2+1=22x2x+1∴\dfrac{{I}_{\max }-{I}_{\min }}{{I}_{\max }+{I}_{\min }}=\dfrac{2\sqrt{{I}_{1}{I}_{2}}}{{I}_{1}+{I}_{2}}=\dfrac{2\sqrt{{I}_{1}/{I}_{2}}}{\dfrac{{I}_{1}}{{I}_{2}}+1}=\dfrac{2\sqrt{2x}}{2x+1}

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