几何法推导斜入射衍射光栅的波长和实验研究

THEORETICAL AND EXPERIMENTAL STUDY ON WAVELENGTH MEASUREMENT OF OBLIQUE INCIDENCE DIFFRACTION GRATING VIA GEOMETRIC OPTICAL METHOD

通过直接几何光路法和光栅方程法分析了平行光斜入射衍射光栅时波长测量的理论基础。分析表明,几何光路法是斜入射衍射光栅问题的一种严格解法,光栅方程法是几何法的一级近似。实验中以低压汞灯的绿光为基准,通过分光计测量平行光斜入射衍射光栅时紫光的波长。具体方法是:先让望远镜分划板的竖准线对准平行光正入射时绿光衍射线位置,然后转动光栅使紫光与准线重合,由光栅转过的角度获得转动前后的光程差,从而计算出待测光的波长。当使用绿光为基准光时,用几何法和光栅方程法得到的紫光波长均为434.9nm,与理论值的相对误差均为0.2%。

The theory of oblique incidence diffraction grating for collimated light is analyzed by using direct geometric light path method and grating equation method.The analysis reveals that geometric optical path method is an exact analytical method for oblique incidence diffraction grating,and the grating equation method is the first-order approximation of the geometric method.In the experiment,based on the green light of low-pressure mercury lamp,the wavelength of violet light from low-pressure mercury lamp was measured by spectrometer when collimated light was obliquely incident to diffraction grating.The detailed method is as follows.Firstly,the vertical directrix of the telescope divider was aligned with the first order green diffraction light for normal incidence.Then,the grating was rotated to make the purple light coincide with the collimation line.The optical path difference before and after the grating rotation was obtained by the angle of grating rotation and thus the wavelength of the violet light was calculated.When green light is used as the reference light,the wavelength of violet light obtained by geometric method and grating equation method is 434.9 nm,and the relative error with the theoretical value is 0.2%.