A 660 nm laser beam passes through a rectangular aperture and forms a central diffraction maximum on a wall 4.50 m away, 110 mm wide and 6.00 mm high. Which pair matches the source answer for the aperture dimensions?
Options

Question

A 660 nm laser beam passes through a rectangular aperture and forms a central diffraction maximum on a wall 4.50 m away, 110 mm wide and 6.00 mm high. Which pair matches the source answer for the aperture dimensions?

Options

G1 Physics · Accepted Answer

For a rectangular aperture, the central diffraction width in a given direction is w=2λD/a. Using λ=660 nm and D=4.50 m: for the 110 mm central width, a=2λD/w=2(660×10⁻⁹)(4.50)/(0.110)=5.4×10⁻⁵ m=54 μm; for the 6.00 mm central height, a=2λD/w=2(660×10⁻⁹)(4.50)/(0.006)=9.9×10⁻⁴ m=0.99 mm. Thus the direct calculation gives 54 μm by 0.99 mm. The source answer sheet, however, prints 5.4 μm by 0.99 mm. To stay source-faithful, option A is stored, with this discrepancy explicitly noted.