What is the angular separation of two spectral lines of wavelengths 497 nm and 251 nm formed in the third order with a diffracting grating having 587 lines per millimeter

34.8°

Explanation:

Given the following :

Number of lines (N) = 587mm

529mm to m = 587*1000 = 587000 per meter

d = 1 / N ; 1/587000 = 0.00000170357

Wavelength of light waves :

λ1 = 497nm = 497 × 10^-9 m

λ2 = 251nm = 251 × 10^-9 m

Angular position in 3rd order; m=3

For

λ1 ; dsinθ3 = 3λ1 ;

λ2 = dsinθ3 = 3λ2

Substituting values

dsinθ3 = 3λ1 =

0.00000189 * sinθ3 = 3 * 497 × 10^-9

θ3(1) = sin^-1(1491 * 10^-9 / 0.00000170357)

θ3(1) = sin^-1(0.8752208)

θ3(1) = 61.07°

λ2 = dsinθ3 = 3λ2

0.00000189 * sinθ3 = 3 * 251 × 10^-9

θ3(2) = sin^-1(753 * 10^-9 / 0.00000170357)

θ3(1) = sin^-1(0.4420129)

θ3(1) = 26.23°

Angular separation :

61.07° - 26.23° = 34.84°

34.8°

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