Final answer:
Comparison of the diffraction patterns for two lasers and two gratings reveals that Grating B must have more lines per millimeter, and if the green laser were shone through Grating B, the first maximum would be more than 1 meter away from the center.
Step-by-step explanation:
To analyze this problem, we need to apply our knowledge of diffraction gratings and wavelength of light. The position of the maxima on the screen depends on the grating spacing (number of lines per millimeter) and the wavelength of the light. The formula for the angle of the maxima for a diffraction grating is:
nλ = d sin θ,
where:
- n is the order of the maximum,
- λ is the wavelength of the light,
- d is the distance between adjacent lines on the grating, and
- θ is the angle of the maximum from the normal.
When comparing two diffraction gratings with different lasers:
- A green laser (shorter wavelength) producing a first maximum at 1 meter suggests that the spacing between lines (d) in grating A supports this particular maximum for that wavelength.
- A red laser (longer wavelength) producing a first maximum at the same distance suggests that grating B must have a smaller d (more lines per mm) to compensate for its longer wavelength to produce a maximum at the same distance.
Hence, the answer is (c):
a) Grating B has more lines/mm; because it compensates for the longer wavelength of the red light to still create a maximum at the same position as the green light with grating A.
b) If the green laser (shorter wavelength) were shone through grating B (more lines/mm), the first maximum would be more than 1 meter away from the center, since a grating with more lines per millimeter spreads the maxima further apart for the same wavelength, compared to a grating with fewer lines per millimeter.