A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young’s double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point

Question

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young’s double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is ________ $\times 10^{- 5}$ m. [2026]

Smart Achievers · Accepted Answer

(429)

$y = n \frac{λ D}{d}$

$y_{1} = y_{2}$

$n_{1} λ_{1} \frac{D}{d} = n_{2} λ_{2} \frac{D}{d}$

$\frac{n_{1}}{n_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{550}{650} = \frac{11}{13}$

$y = 11 \times \frac{λ_{1} D}{d} = \frac{11 \times 650 \times 10^{- 9} \times 1.2}{2 \times 10^{- 3}}$

$y = 429 \times 10^{- 5}$

Solution

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Solution

Ans. (429) y=nλDd y1=y2 n1λ1Dd=n2λ2Dd n1n2=λ2λ1=550650=1113 y=11×λ1Dd=11×650×10-9×1.22×10-3 y=429×10-5

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