Wave Optics

JEE Main level, numerical answer, medium

84 of 191

Question 84 of 191

White light is passed through a double slit and interference is observed on a screen 1.5m1.5m away. The separation between the slits is 0.3mm0.3mm. The first violet and red fringes are formed 2.0mm2.0mm and 3.5mm3.5mm away from the central white fringes. The difference in wavelengths of red and violet light is (innm).\left(\text{in}nm\right).

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Answer: 300

y1=λrDd{y}_{1}=\dfrac{{\lambda }_{r}D}{d}
y2=λvDd{y}_{2}=\dfrac{{\lambda }_{v}D}{d}
λr−λv=(y1−y2)dD=(3.5−2)mm×0.3mm1.5m=300nm{\lambda }_{r}-{\lambda }_{v}=\left({y}_{1}-{y}_{2}\right)\dfrac{d}{D}=(3.5-2)mm\times \dfrac{0.3mm}{1.5m}=300nm

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