A monochromatic beam of light of wavelength 698 nm is incident at 90° to the plane of a diffraction grating. The second-order image is observed at a diffraction angle of 56.7°. The light source is replaced with another monochromatic beam, which has a different wavelength. The third-order image is now observed to have the same diffraction angle (56.7°) as the second-order image had previously. (i) Calculate the wavelength of the second light source. (ii) Calculate the grating spacing of the diffraction grating. (iii) Derive an expression (in terms of wavelength, A, and grating spacing, d) for the theoretical maximum number of diffraction orders, nmax, that can be seen either side of the straight-through position. Comment on the values that nmax can take. (iv) Will a larger or smaller number of diffraction orders be obtained if the light sources are now replaced by a source of infrared radiation. Explain your answer.

A monochromatic beam of light of wavelength 698 nm is incident at 90° to the plane of a diffraction grating. The second-order image is observed at a diffraction angle of 56.7°. The light source is replaced with another monochromatic beam, which has a different wavelength. The third-order image is now observed to have the same diffraction angle (56.7°) as the second-order image had previously. (i) Calculate the wavelength of the second light source. (ii) Calculate the grating spacing of the diffraction grating. (iii) Derive an expression (in terms of wavelength, A, and grating spacing, d) for the theoretical maximum number of diffraction orders, nmax, that can be seen either side of the straight-through position. Comment on the values that nmax can take. (iv) Will a larger or smaller number of diffraction orders be obtained if the light sources are now replaced by a source of infrared radiation. Explain your answer.