A single slit diffraction pattern is formed with white light. For what wavelength of light the 4^ th secondary maximum in diffraction pattern coincides with the 3^ rd secondary maximum in the pattern of light of wavelength ' ' ?

Step-by-step solution

To determine the condition for secondary maxima coincidence in single-slit diffraction , use the general formula a = (n + 1 2 ) , where a is the slit width, is the diffraction angle, n is the order (starting at n=1 for the first secondary maximum), and is the wavelength. For the 4^ th secondary maximum of wavelength ' at angle ₁ : a ₁ = (4 + 1 2 ) ' = 9 2 ' For the 3^ rd secondary maximum of wavelength at angle ₂ : a ₂ = (3 + 1 2 ) = 7 2 Since the angular positions coincide, ₁ = ₂ , equating the two expressions: 9