The condition of diffraction is given by the following equation.
dsinθ=mλ
d – is the split separation
m – is the order of diffraction
λ is the wavelength
θ is the diffraction angle
The slit separation d is the reciprocal of total number of lines N on the grating.
d=N1
d=15000lines/inch1
=6.666×10−5inch(1inch2.54cm)
=1.69×10−4cm
θ=sin−1(dmλ)
m =1
λ = 598 nm
θ=sin−1(1.69×10−41×598.0×10−7)=20.7º
∆θ=dcosθm∆λ
∆λ = 589.6 – 589.0 = 0.6 nm
∆θ=1.69×10−4cos(20.7)10.6×10−7=3.795×10−4radians
The separation between the lines of sodium is equal to the product of focal length and angular width.
∆d = f∆θ
f = 10 cm
∆d=10×3.795×10−4=0.03795mm
The separation between the lines of sodium is 0.038 mm.
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