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How aperture affects depth of field. · Control depth of field with aperture. · Change how much your camera sees with focal length. · Use aperture and focal length ...

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with the sign convention as noted. n is the diffraction order and says by how many wavelengths the wavefront shifts between incidence and scattering. If the grating acts as a mirror, n = 0. Dispersion, different wavelengths giving constructive interference at different angles, requires that n be a non-zero integer. Since the sine of an angle is always of magnitude less than 1, the largest value of λ for which there is a solution for the grating equation is for n = 1, sin α = 1, sin β = 1, so λ = 2d.

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If we say: all angles are measured counter-clockwise, starting at the grating normal, then in the above drawings, α is positive and β is negative. For constructive interference to occur, we know that the phase shift in scattering from adjacent echellettes must be an integer number of wavelengths (so the crests of the scattered waves from the two facets are in-phase). This leads to The Grating Equation: