A monochromatic light of wavelength `500 nm` is incident normally on a single slit of width `0.2 mm` to produce a diffraction pattern. Find the angular width of central maximum obtained on the screen, `1 m` away. Estimate the number of fringes obtained in YDSE with fringe width `0.5 mm`, which can be accommodated within the region of total angular spread of the central maximum due to a single slit.
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Here, `lambda = 500 nm = 5 xx 10^(-7) m` , `a = 0.2 mm = 2 xx 10^(-4)m, D = 1 m` Angular width of central maximum `= (2 lambda)/(a) = (2 xx 5 xx 10^(-7))/(2 xx 10^(-4)) = 5 xx 10^(-3) radian` Width of central maximum `= (2 lambda D)/(a)` `= 5 xx 10^(-3) xx 1m` As `beta = 0.5 mm = 5 xx 10^(-4)m` `:.` Number of interference fringes in the central maximum, `n = (5 xx 10^(-3))/(5 xx 10^(-4)) = 10`
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