Angular width of central maximum in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000Å.Case-1 : When the slit is illuminated by light of another wavelength, the angular width decreases by 30%.Case-2 : When the original apparatus is immersed in a liquid, angular width decreases by 30%.Choose the correct option(s) :In case 1, wavelength of light is 4800Å.In case 1, wavelength of light is 4200Å.In case 2, refractive index of liquid is 1.25.In case 2, refractive index of liquid is 1.43.
Question
Angular width of central maximum in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000Å.Case-1 : When the slit is illuminated by light of another wavelength, the angular width decreases by 30%.Case-2 : When the original apparatus is immersed in a liquid, angular width decreases by 30%.Choose the correct option(s) :In case 1, wavelength of light is 4800Å.In case 1, wavelength of light is 4200Å.In case 2, refractive index of liquid is 1.25.In case 2, refractive index of liquid is 1.43.
Solution
The angular width of the central maximum in the Fraunhofer diffraction pattern is given by the formula θ = λ/a, where λ is the wavelength of the light and a is the width of the slit.
Case 1: If the angular width decreases by 30%, the new wavelength λ' is 70% of the original wavelength. So, λ' = 0.7 * λ = 0.7 * 6000Å = 4200Å. Therefore, the statement "In case 1, wavelength of light is 4200Å" is correct, and the statement "In case 1, wavelength of light is 4800Å" is incorrect.
Case 2: The refractive index n of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium. When light enters a medium with a higher refractive index, its speed and wavelength decrease, but its frequency remains the same. If the angular width decreases by 30% when the apparatus is immersed in a liquid, the refractive index n' of the liquid is 1/0.7 times the refractive index of air (which is approximately 1). So, n' = 1/0.7 = 1.43. Therefore, the statement "In case 2, refractive index of liquid is 1.43" is correct, and the statement "In case 2, refractive index of liquid is 1.25" is incorrect.
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