A diffraction grating produces a second-order bright spot for red light (wavelen

Question

A diffraction grating produces a second-order bright spot for red light (wavelength of 700 nm) at an angle of 40 degrees from the central maximum. (1) For what wavelength will the third-order bright spot be produced at the same angle? (2) Now replace the diffraction grating with a screen with two narrow slits in it. spaced 2.3 pm apart and placed 45m from another screen on which light is collected. What is the distance between the first and second bright lines of the interference pattern when the slits are illuminated with light with a wavelength of 550 nm?

Explanation / Answer

given,

wavelength = 700 nm

angle = 40 degree

since,

m lambda = d sin theta

2 * 700 * 10^-9 = d * sin(40)

d = 2178 nm

for third order bright spot

3 * wavelength = 2178 * sin(40)

1) wavelength = 466.66 nm

Displacement y = (Order m x Wavelength x Distance D)/(slit width a)

distance between second and first bright lines = (2 x Wavelength x Distance D)/(slit width a) - (1 x Wavelength x Distance D)/(slit width a)

distance between second and first bright lines = (1 x Wavelength x Distance D)/(slit width a)

distance between second and first bright lines = (1 * 550 * 10^-9 * 4.5)/(2.3 * 10^-6)

2) distance between second and first bright lines = 1.076 m

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