Using monochromatic light of wavelength λ , an experimentalist sets...

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

Options

A520 nm
B580 nm
C540 nm
D560 nm

Correct answer

C. 540 nm

Step-by-step solution

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

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

Now shift

= \dfrac{\left(\mu - 1\right) \text{t D}}{\text{d}}

y = {\beta}^{1}

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

\lambda = \dfrac{\left(\mu - 1\right) \text{t}}{2} = \dfrac{\left(\text{1.6} - 1\right) \times \text{1.8}}{2}

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

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

= \text{0.54} \mu \text{m}

= 540 nm

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