Laser light of wavelength 632nm is incident on a diffraction grating having
600 lines per mm. Determine the angular separation between the first and second
order maxima
310
To determine the angular separation between the first and second order maxima in a diffraction grating, we need to use the equation for the angular position of the maxima given by the grating equation:
sinθ = mλ / d
Where:
- θ is the angle between the incident light and the diffracted light
- m is the order of the maximum
- λ is the wavelength of the incident light
- d is the spacing between the lines on the grating
Given:
- Wavelength of the laser light (λ) = 632 nm
- Number of lines per mm (N) = 600
Firstly, we need to calculate the spacing between the lines on the grating (d):
Spacing (d) = 1 / N
Substituting the value of N into the equation, we get:
d = 1 / 600 mm = 1.67 × 10^(-3) mm
Next, we can calculate the angle for the first order maximum (m = 1) using the grating equation:
sinθ₁ = (1 * λ) / d
Substituting the values, we get:
sinθ₁ = (1 * 632 nm) / (1.67 × 10^(-3) mm)
To convert mm to nm, we need to multiply by 10^6 (1 mm = 10^6 nm):
sinθ₁ ≈ (1 * 632 × 10^6 nm) / (1.67 mm)
Now, we can calculate the angle for the second order maximum (m = 2) using the same process:
sinθ₂ = (2 * λ) / d
Substituting the values, we get:
sinθ₂ = (2 * 632 nm) / (1.67 × 10^(-3) mm)
To convert mm to nm, we need to multiply by 10^6 (1 mm = 10^6 nm):
sinθ₂ ≈ (2 * 632 × 10^6 nm) / (1.67 mm)
Finally, we can calculate the angular separation between the first and second order maxima (Δθ):
Δθ = θ₂ - θ₁
Substituting the values of sinθ₁ and sinθ₂ into the equation, we get:
Δθ = arcsin(sinθ₂) - arcsin(sinθ₁)
Calculating this difference will give you the angular separation between the first and second order maxima.