Problem 2. In diffraction experiments involving multiple wavelengths of light passing through the same aperture, the...

Problem 2. In diffraction experiments involving multiple wavelengths of light passing through the same aperture, the higher order maxima of one wavelength can coincide with a lower order maxima of a longer wavelength. In the above diffraction experiment, the 3rd maxima of 600 nm light is found to coincide with the 4th maxima of a different wavelength of light. What is the other wavelength?

Expert Solution

Given m₃ = 3, ₃ = 600nm and m₄ = 4, ₄ = ?

We know that for a grating having grating element ( a + b ) the angle of diffraction in the m^th order spectrum for a light of wavelength is given by

( a + b ) sin() = m

for a given grating ( a + b ) is constant i.e., same aperture and hence will be the same when m is constant.

m = constant

=> m₃₃ = m₄₄

=> 3 x 600nm = 4 x ₄

=> ₄ = 450nm

the other wavelength is 450nm

genius_generous answered 7 months ago

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