Question

3. (20 points) A monochromator is a popular choice of wavelength selector in optical instruments. Answer the following question regarding a monochromator that has a focal length of 0.78 m and a grating of 2500 lines/mm. (a) (b) Draw a schematic diagram to show key elements in any monochromator, including slits, reflectors and grating. Describe briefly how each element affects the resolution in wavelength at the output of monochromator. Calculate the reciprocal linear dispersion (D-1) of the monochromator for the first and second order spectra, respectively. If a 2.0-cm grating is illuminated, calculate the first and second order resolving power (R) of the monochromator. At around 410 nm, associated with the heme absorption, what minimum wavelength difference (in nm) can be completely resolved by the instrument?

Answer 1

|(b) The grating has 2,500 blazes/mm. The relationship between the reciprocal linear dispersion ( D-1), the focal length f, the order of the diffraction n and the distance between blazes (d) is given by the following equation. D-I = d Substitute the value of the focal length f(0.78 m), the order of the diffraction n (1) and the 1 mm distance between rulings (d) ( =) in the above equation 2,500 lines ( 1 mm D-1 - (2,500 lines 1x(0.78 m) nm - (2,500 lines ) (100 mm) 2,500 lines mm 1x(0.78 m )x(108 prend = 0.51 nm mm nm Therefore, the reciprocal linear dispersion ( D-1) for the first order diffraction is 0.51 mm

|(c)2.0 с of grating is illuminated The number N of grating lines illuminated is as calculated below N 2,500 lines x 20 cm = 1 mm = 50,000 lines 1 * 10 mm x 10 - em

The resolving power of a grating (R) is given by the following equation R = nN Where n is the diffraction order and N is the number of grating lines illuminated.

Substitute the value of the diffraction order n (1) and the number Nof grating lines illuminated in the above equation R = nN = 1 x 50,000 lines = 50,000 Therefore, the first order resolving power is 50,000

lid) The wavelength (a) is 410 nm. The resolving power of the grating is as given below R =- M = 50,000 Substitute the value of the wavelength (a) in the above equation 410 nm 50,000 M2 Rearrange the above equation 410 nm M = 50,000 = 8.2 x 10 nm Therefore, the minimum wavelength difference that can be theoretically completely resolved by the instrument is 8.2x10-3 nm ·