Question

A single slit of width d = 0.08 mm is illuminated by light of two wavelengths, l = 446 nm and l = 662 nm. The diffraction pattern appears on a screen 1.05 m away. (a) Calculate the angles at which the third dark fringe appears for each wavelength. q446 = rad q662 = rad (b) Calculate the width of the central bright fringe for each wavelength. d446 = m d662 = m

Answer 1

Answer

given,

width of slit, d = 0.08 mm

                   d = 8 x 10⁻⁵ m

light of two wavelength

I₁= 446 nm

I₂ = 662 nm

a)  angles at which the third dark fringe

    $sin C = \dfrac{m\lambda}{d}$

                m = 3  , I₁= 446 nm

    $sin C = \dfrac{3\times 446 \times 10^{-9}}{8\times 10^{-5}}$

                 C = 0.958°

                m = 3  , I₁= 662 nm

    $sin C = \dfrac{3\times 662 \times 10^{-9}}{8\times 10^{-5}}$

                 C = 1.423°

b)  angles at which the third dark fringe

    $sin C = \dfrac{m\lambda}{d}$

                m = 1  , I₁= 446 nm

    $sin C = \dfrac{1\times 446 \times 10^{-9}}{8\times 10^{-5}}$

                 C = 0.319°

                m = 1  , I₁= 662 nm

    $sin C = \dfrac{1\times 662 \times 10^{-9}}{8\times 10^{-5}}$

                C = 0.474°