In a university optics lab, a narrow rectangular slit of unknown width is illuminated simultaneously by two lasers, one red and one green. The red laser has a known wavelength of λr=632nm, whereas the green laser’s wavelength λg is to be determined. Both beams are normally incident on the slit and project overlapping diffraction patterns onto a screen L=1.80m away. A light-sensitive screen records the combined intensity distribution, and the resulting graph of intensity I versus lateral distance y (measured from the central maximum) is printed on logarithmic intensity paper. The central maximum for each color appears at y=0 on the same vertical line.
After careful analysis of the graph, the following features are extracted:
• For the red laser, the first minimum occurs at y=±2.15mm.
• For the green laser, the first minimum occurs at y=±1.72mm.
• The peak intensity of the green central maximum is 1.8 times the peak intensity of the red central maximum, as read from the logarithmic scale.
Assume both lasers have the same power output at the slit, the detector responds linearly to power, and both patterns follow ideal single-slit behaviour.
(a) Determine the width of the slit, stating all steps and keeping at least three significant figures.
(b) Using your result from part (a), calculate the wavelength λg of the green laser.
(c) The ratio of peak intensities suggests that the green beam experiences greater diffraction loss through the slit than the red beam. Provide a quantitative explanation consistent with single-slit theory that accounts for the observed intensity ratio.
(d) Briefly discuss one advantage and one limitation of using a logarithmic intensity scale when analysing overlapping diffraction patterns such as these.