Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength `6000Å`. When the slit is illuminated by light of another wavelength, the angular width decreases by `30%`. Calculate the wavelength of this light. The same decrease in the angular width of central maximum is obtained when the original apparatus is immersed in a liquid. Find the refractive index of the liquid.
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If `lambda` is wavelength of light used and a is the width of the slit, then angular width of central maximum, `2 theta_(1) = (2 lambda)/(a)`. With light of another wavelength `lambda'`, width of central maximum, `2theta'_(1) = (2 lambda')/(a)` As `2 theta_(1) = (70)/(100)(2 theta_(1))` `:. (2lambda')/(a) = (7)/(10)(2lambda)/(a)` `lambda' = (7)/(10) xx 6000 Å = 4200 Å` If the same change in angular width of central maximum is obtained by immersing the apparents in a liquid, then `lambda' = (lambda)/(mu) or mu = (lambda)/(lambda') = (6000)/(4200) = 1.429`
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