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JEE Main 2023 (6 Apr, Shift 2) · YDSE: Film, Medium & Two Wavelengths

YDSE: Film, Medium & Two Wavelengths question from JEE Main 2023 (6 Apr, Shift 2)

Q45JEE Main 2023 · 6 APR · SHIFT 2Medium

YDSE: Film, Medium & Two Wavelengths

A beam of light consisting of two wavelengths 7000 A˚7000\ \text{\AA} and 5500 A˚5500\ \text{\AA} is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm2.5\text{ mm} and the distance between the plane of slits and the screen is 150 cm150\text{ cm}. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is n×10−5 mn \times 10^{-5}\text{ m}. The value of nn is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 462

  1. Coincidence: n1×7000=n2×5500⇒14n1=11n2n_1 \times 7000 = n_2 \times 5500 \Rightarrow 14n_1 = 11n_2, so n1=11n_1 = 11.
  2. y=11×7×10−7×1.52.5×10−3=4.62×10−3 my = \dfrac{11 \times 7\times10^{-7} \times 1.5}{2.5\times10^{-3}} = 4.62\times10^{-3}\text{ m}
  3. So n=462n = 462.
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