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Figures (3)

Fig. 1

A typical plane grating spectrograph showing the entrance slit S, collimator C, diffraction grating G, and mirror M. The angles x and y are angles of incidence and diffraction. The angle α is the angle between the mirrors as viewed from the grating. The solid lines represent the optical path for wavelength λ, the dashed lines for wavelength λ′. β and δ are the changes in angle for unit wavelength difference as the result of single and double-pass dispersions, respectively.

Fig. 2

Relative dispersion at various wavelengths for a 300 lines/mm grating. Curve A is for i = θ + 10° in single pass or i = θ − 10° in double pass. Curve B is for i = θ − 10° in single pass or i = θ + 10° in double pass. The dashed curve is for i = θ. The angles i and θ are the angles of incidence and diffraction for the first diffraction in a double-pass system.

Fig. 3

Relative intensities for various orders of λ5460 for several values of α, the angle between the mirrors of the spectrograph viewed from the grating.

Equations (3)

$m λ / d = a = sin x + sin y , m λ ′ / d = a ′ = sin x + sin ( y + β ) , a ′ = sin ( y - β ) + sin ( x + δ ) , a ′ = sin y + sin ( x + β ′ ) , a ′ = sin ( x - β ′ ) + sin ( y + δ ′ ) .$
$β = a ′ - a cos y = Δ λ d cos y , β ′ = a ′ - a cos x = Δ λ d cos x , δ = 2 cos y cos x β = 2 β ′ , δ ′ = 2 cos x cos y β ′ = 2 β .$
$R . P . = ν d ν = ν W P ( sin i + sin θ ) = W P m d ,$