In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength 6480 Å , angular width of central maximum is measured. When the slit is illuminated by light of another wavelength ' ' the angular width decreases by 25 % . The value of in Å units is

Step-by-step solution

The angular width of the central maximum in a single slit Fraunhofer diffraction is given by = 2 a , where is the wavelength of light and a is the width of the slit. From this relation, the angular width is directly proportional to the wavelength, . Let the initial wavelength be ₁ = 6480 Å with angular width ₁ . When the angular width decreases by 25 % , the new angular width becomes ₂ = ₁ - 0.25 ₁ = 0.75 ₁ . Since , the new wavelength is given by = 0.75 ₁ . Substituting the given value of ₁ : = 0.75 6480 = 3 4 648