Here, distance between two slits, d = 1 mm = 10⁻³ m, distance of screen from slits, D = 1 m, wavelength of monochromatic light used, λ = 500 nm = 500 × 10⁻⁹ m. Width of central maxima in single slit pattern is 2λD/a. Fringe width in double slit experiment β = λD/d. Calculate the required c

Question

Here, distance between two slits, d = 1 mm = 10⁻³ m, distance of screen from slits, D = 1 m, wavelength of monochromatic light used, λ = 500 nm = 500 × 10⁻⁹ m. Width of central maxima in single slit pattern is 2λD/a. Fringe width in double slit experiment β = λD/d. Calculate the required condition for width of central maxima.

Accepted Answer

2λD/d = λD/a. The width of the central maximum in a single-slit diffraction pattern is given by 2λD/a, and the fringe width in a double-slit experiment is β = λD/d. For the width of the central maximum to equal the fringe width, we equate 2λD/a = λD/d, which simplifies to 2/d = 1/a or 2λD/d = λD/a.

Solution

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