Grating normal

Figure 1. Layout of a generic spectrograph employing a reflection grating. Angles a and (3 have the same sign if they are on the same side of the grating normal. Inset the condition for interference of light by a diffraction grating.

The following definitions are required 6g is the angle between a ray parallel to the collimator axis and the grating normal, the angle of incidence 8 = 0g + Si9 and the diffraction angle 9d = 9g — 5d. In the symmetrical Littrow case 5 = — <5d, and Eq. (3) follows from the general grating equation... 

The plus sign is taken if A and B are on the same side of the grating normal and the minus sign if they are not. If the light is reflected back into the direction of the incident light, the equation reduces to ... 

Figure 25-8 Mechanism of diffraction from an echellette-type grating. Angle i from the grating normal is the angle of the incident beam angle r is the angle of the reflected beam. The distance between successive rulings is d.

In Figure 25-8, parallel beams of monochromatic radiation labeled 1 and 2 are shown striking two of the broad faces at an incident angle i to the grating normal. Maximum constructive interference occurs at the reflected angle r. Beam 2 travels a greater distance than beam 1 this difference is equal to CB + BD. For constructive interference to occur, this difference must equal nA.-... 

Note that when diffraction occurs to the left of the grating normal, values of n are positive, and when diffraction occurs to the right of the grating normal, n is negative. Thus, n = 1, 2, 3, and so forth. 

Calculate the number of grooves/mm for a Littrow grating for a 25° incidence at X = 488nm (i.e., the first diffraction order is being reflected back into the incident beam at an angle a = 25° to the grating normal). 

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