Final answer:
The second-order diffraction angle for a grating with 550 slits per mm and a first-order diffraction angle of 27.8° is approximately 0.1°.
Step-by-step explanation:
The formula to calculate the diffraction angle for a diffraction grating is given by:
sin(θ) = mλ/d
Where:
- θ is the diffraction angle
- m is the order of diffraction
- λ is the wavelength of the light
- d is the spacing between the grating slits
In this case, we are given the first-order diffraction angle and the number of slits per mm. To find the second-order diffraction angle, we can use the same formula, but with m = 2.
Let's plug in the values:
sin(θ) = 2⋅550⋅10-3/550 = 2⋅10-3
Now, we can solve for θ:
θ = arcsin(2⋅10-3) ≈ 0.1146°
Therefore, the second-order diffraction angle is approximately 0.1°.