Wave Optics

JEE Main level, single correct, medium

110 of 191

Question 110 of 191

Using monochromatic light of wavelength λ\lambda, an experimentalist sets up the Young's double slit experiment in three ways as shown.
If she observes that y⁡=β′y⁡={\beta }^{'}, the wavelength of light used is :

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Answer: (C) 540 nm

β=λDd.\beta =\dfrac{\lambda \text{D}}{\text{d}\text{.}}

∴β1=λ2Dd.∴{\beta }^{1}=\dfrac{\lambda 2\text{D}}{\text{d.}}

Now shift =(μ−1)t Dd=\dfrac{\left(\mu -1\right)\text{t D}}{\text{d}}

y=β1y={\beta }^{1}

(μ−1)t Dd=λ.2Dd\dfrac{\left(\mu -1\right)\text{t D}}{\text{d}}=\dfrac{\lambda \text{.}2\text{D}}{\text{d}}

λ=(μ−1)t2=(1.6−1)×1.82\lambda =\dfrac{\left(\mu -1\right)\text{t}}{2}=\dfrac{\left(\text{1.6}-1\right)\times \text{1.8}}{2}

=0.6×1.82μm=\dfrac{\text{0.6}\times \text{1.8}}{2}\mu \text{m}

=0.3×1.8μm=\text{0.3}\times \text{1.8}\mu \text{m}

=0.54μm=\text{0.54}\mu \text{m}

= 540 nm

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