A diffraction grating has 5580 lines/cm . When a beam of monochromatic light goe

Question

A diffraction grating has 5580 lines/cm . When a beam of monochromatic light goes through it, the second pair of bright spots occurs at (+ or -) 26.3 cm from the central spot on a screen 42.5 cm past the grating.

a.)What is the wavelength of this light (in nm)?

b.)How far from the central spot does the next pair of bright spots occur on the screen (in degrees)?

{question a. should=472 nm and question b. should =54.7 cm}

If anyone could help me solve this it would be greatly appreciated, Thank you.

Explanation / Answer

d=1/5580*10^2 =1.792*10^-6 m

tan(x) =Y/D =26.3/42.5

x=tan^-1(26.3/42.5)

x=31.75 degrees

dsin(x) =mlambda

here m=2

1.79*10^-6*sin31.75 =2*lambda

lambda =4.715*10^-7 m =471.5*10^-9 m

lambda=471..5 nm =472 nm(approx)

b)

Now m=3

dsin(x) =m*lambda

1.792*10^-6*sin(x)=3*472*10^-9

x=52.12 degrees

tan(x)=Y/D

Y=Dtan(x) =42.5*tan(52.12)

Y=54.65 cm

Y=54.7 cm (approx)

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