White light is passed through a double slit and interference is observed on a screen \(1.5 \,{m}\) away. The separation between the slits is \(0.3 \,{mm}\). The first violet and red fringes are formed \(2.0 \,{mm}\) and \(3.5\, {mm}\) away from the central white fringes. The difference in wavelengths of red and voilet light is \(.... \,{nm} .\)

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Answer & Solution

Correct Answer

(C) \(300\)

Detailed explanation

Position of bright fringe \({y}={n} \frac{{D} \lambda}{{d}}\)

\({y}_{1} \text { of red }=\frac{{D} \lambda_{{r}}}{{d}}=3.5\, {mm}\)

\(\lambda_{{T}}=3.5 \times 10^{-3} \frac{{d}}{{D}}\)

Similarly \(\lambda_{{v}}=2 \times 10^{-3} \frac{{d}}{{D}}\)

\(\lambda_{{r}}-\lambda_{{v}}=\left(1.5 \times 10^{-3}\right)\left(\frac{0.3 \times 10^{-3}}{1.5}\right)\)

\(=3 \times 10^{-1}=300\, {nm}\)

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