Final answer:
Increasing the number of lines per centimeter on a diffraction grating leads to a more finely spaced interference pattern, while using a longer-wavelength light spreads the pattern farther apart. These changes are consistent with the diffraction equation relating slit spacing and wavelength to the angle of the maxima.
Step-by-step explanation:
When pure-wavelength light falls on a diffraction grating with more lines per centimeter, the interference pattern becomes more finely spaced. This is because increasing the number of lines per centimeter essentially decreases the slit spacing, leading to larger angles for the interference maxima.
Specifically, the equation d sin(θ) = mλ, where d is the slit spacing, θ is the angle of the diffraction maxima, m is the order of the maximum, and λ is the wavelength of the light, explains this behavior. A greater number of lines means smaller d, leading to larger θ for any given m and λ.
If a longer-wavelength light falls on the same grating, the interference maxima will spread farther apart. Again, using the same equation, we see that for the same grating (fixed d) an increase in λ will lead to larger θ values for the diffraction maxima, indicating the pattern spreads out more.
These two effects demonstrate how variations in the number of grating lines and light wavelength directly influence the interference pattern, which shows consistency in the relationship of wavelength to the distance between slits. Adjusting either the grating density or the wavelength adjusts the angle θ at which maxima are found, thus affecting the overall diffraction pattern observed.