Requesting help with units of angular dispersion for reflection grating

[jhbrown]

Dear ACS members,

Could someone please explain the units of angular dispersion for a reflection grating? The equation is Da = n / d * cos(r). An optics book listed the units: Da is angular dispersion (radians/nm), n is the reflection order (unitless), d is the spacing between rulings (nm), cos(r) is the cosine of the reflected angle, and r is the reflection angle (degrees). I do not understand where the radians come from in the result given the units of the calculation. This is the only book I could find the units specifically listed. Is this a misprint?

Thank you,

Jay Brown

[jhbrown]

An expert in the field helped with the issue. The unit of angular dispersion for a reflection grating is nm^-1 when the spacing of the rulings is nm. That makes perfect sense given the units used in the equation. To convert to radians/nm, you need to multiply the result by pi radians (half a circle for a reflection grating). This detail was left out of my textbooks and no examples provided. I want to express my sincere thanks to the person who helped to resolve the confusion.  Jay.