Chapter 14: Superposition of waves
4 A diffraction grating has 500 lines per millimetre. Light is incident normally on the grating. a Calculate the distance, in metres, between one line and the next on the diffraction grating. b Calculate the wavelength of light that gives a first-order maximum at an angle of 22.0º. c Calculate the angle of the second-order maximum when light of this wavelength is used. d State what happens when you try to use the diffraction grating formula for the third-order. This limits the number of orders to only two in this case. e State the total number of lines seen in the diffraction pattern if only two orders are present in the spectrum of a monochromatic source of light. 5 Light of wavelength 590 nm is incident normally on a diffraction grating of width 30.0 mm which contains 10 000 lines. a Calculate the spacing of the lines in the grating. b Calculate the angular positions of the various orders. 6 When red light of wavelength 700 nm is passed normally through a diffraction grating, the first-order maximum is found at an angle of 25º to the zero-order beam. a Calculate the grating spacing and the number of lines per millimetre in the grating. b Calculate the angle for the first-order maximum using blue light of wavelength 400 nm. c Calculate the difference in angle between the blue light and the red light in the first-order spectrum. 7 Light of wavelength 600 nm is incident normally on a diffraction grating, as shown: 87
screen
diffraction grating light
A θ
B
80 cm
C 150 cm
First order maxima are seen at positions A and C on the screen. a Calculate the angle θ. b Calculate the grating spacing. c Calculate the distance on the screen between B and the position of a second-order maximum.