phy diffraction of light

a) λ of yellow light = 3 x 108/(5.5 x 1014) = 5.45 x 10-7 m

Using s sin θ = nλ with n = 1, we have:

(5 x 10-6)sin θ = 5.45 x 10-7

sin θ = 0.109

θ = 6.26

So the distance between it and the central bright fringe is 2 tan θ = 0.219 m

b) λ of red light = 3 x 108/(4.3 x 1014) = 6.98 x 10-7 m

Using s sin θ = nλ with n = 2, we have:

(5 x 10-6)sin θ = 2 x 6.98 x 10-7

sin θ = 0.279

θ = 16.2

So the distance between it and the central bright fringe is 2 tan θ = 0.581 m

c) λ of violet light = 3 x 108/(7.5 x 1014) = 4 x 10-7 m

Using s sin θ = nλ with n = 3, we have:

(5 x 10-6)sin θ = 3 x 4 x 10-7

sin θ = 0.24

θ = 13.89

So the distance between it and the central bright fringe is 2 tan θ = 0.494 m

(a) use formula: a.sin(theta) = m入
where a is the grating line spacing
(theta) is the angular position of bright fringe of order m
入 is the wavelength of light

(a) wavelength of yellow light = 3x10^8/5.5x10^14 m = 5.45x10^-7 m

hence, 5x10^-6.sin(theta) = 5.45x10^-7
(theta) = 6.26 degrees
Thus, distance from central bright fringe = 2 x tan(6.26) m = 0.22 m

(b) wavelength of red light = 3x10^8/4.3x10^14 m = 6.98x10&-7 m

hence, 5x10^-6.sin(theta) = 2 x (6.98x10^-7)
(theta) = 16.2 degrees
Thus, distance from central bright fringe = 2 x tan(16.2) m = 0.58 m

(c) wavelength of violet light = 3x10^8/7.5x10^14 m = 4 x10^-7 m

hence, 5x10^-6.sin(theta) = 3 x (4x10^-7)
(theta) = 13.89 degrees
Thus, distance from central bright fringe = 2 x tan(13.89) m = 0.49 m