The angular wavelength dispersion relation in a diffraction grating is d sin θ = m λ. What does d represent?

The angular wavelength dispersion relation in a diffraction grating is d sin θ = m λ. What does d represent?

• A. The angle of the diffracted beam
• B. The wavelength of the incident light
• C. The slit spacing (grating spacing)
• D. The order number m

Answer: (C)

In a diffraction grating, the angles at which bright fringes appear are set by how closely the slits are spaced. In that equation, d represents the spacing between adjacent slits on the grating (the grating spacing). It’s the distance from one slit to the next, and it’s related to the groove density by d ≈ 1/(lines per unit length). If the slits are closer together (smaller d) while the light wavelength and the order stay the same, the angle at which a given bright fringe occurs must increase to satisfy d sin θ = m λ, so sin θ grows. Conversely, spreading the slits farther apart (larger d) moves the maxima to smaller angles. The angle θ is what you measure, the wavelength λ is a property of the light, and m is the order of the maximum; d is specifically the slit spacing, not the angle, not the wavelength, and not the order.

In a diffraction grating, the angles at which bright fringes appear are set by how closely the slits are spaced. In that equation, d represents the spacing between adjacent slits on the grating (the grating spacing). It’s the distance from one slit to the next, and it’s related to the groove density by d ≈ 1/(lines per unit length). If the slits are closer together (smaller d) while the light wavelength and the order stay the same, the angle at which a given bright fringe occurs must increase to satisfy d sin θ = m λ, so sin θ grows. Conversely, spreading the slits farther apart (larger d) moves the maxima to smaller angles. The angle θ is what you measure, the wavelength λ is a property of the light, and m is the order of the maximum; d is specifically the slit spacing, not the angle, not the wavelength, and not the order.