Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 A ˚ . When the slit is illuminated by light of anothe

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Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 A ˚ . When the slit is illuminated by light of another wavelength, then the angular width decreases by 30% . The same decrease in angular width of central maximum is obtained when the original apparatus is immersed in a liquid. The refractive index of the liquid will be

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Given, λ 1 ​ = 6000 A ˚ , λ 2 ​ = ? Angular width of central maximum = a 2 λ ​ θ 1 ​ = a 2 λ 1 ​ ​ ....(i) and θ 2 ​ = a 2 λ 2 ​ ​ ∵ θ 2 ​ = θ 1 ​ × 0.7 ∴ θ 1 ​ × 0.7 = a 2 λ 2 ​ ​ .....(ii) From Eqs. (i) and (ii), we get 0.7 1 ​ ⇒ λ 2 ​ ​ = λ 2 ​ λ 1 ​ ​ = λ 1 ​ × 0.7 = 6000 × 0.7 = 4200 A ˚ ​ when immersed in liquid, λ 2 ​ ∵ θ 2 ​ ​ = μ λ 1 ​ ​ = θ 1 ​ × 0.7 ​ ⇒ a 2 λ 2 ​ ​ = a 2 λ 1 ​ ​ × 0.7 [ ∵ λ 2 ​ = μ λ 1 ​ ​ ] ⇒ ⇒ ​ a 2 λ 1 ​ / μ ​ μ 1 ​ ​ = a 2 λ 1 ​ ​ × 0.7 = 0.7 ⇒ μ = 1.42 ​

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