Final answer:
Increasing the number of slits in a diffraction grating from 2 to 50 sharpens the interference pattern, resulting in narrower, more distinct principal maxima and an overall more detailed pattern.
Step-by-step explanation:
When the number of slits in a diffraction grating is increased from 2 to 50, while keeping the distance between the slits the same, the interference pattern changes significantly. The primary effect of adding more slits is to produce a greater number of narrower and sharper principal maxima, making the pattern more detailed. According to the equation for constructive interference, d sin θ = mλ (where d is the distance between slits, λ is the wavelength of light, and m is the order of the maximum), increasing the number of slits results in a higher number of bright fringes with increased sharpness and reduced intensity in between them. This sharpness is because the more slits there are, the more constructive interference peaks there will be, and similarly, the destructive interference crests will be more pronounced, leading to a more distinguished pattern. In summary, the pattern becomes sharper with more distinct maxima and more detailed interference, creating an improved distinguishability of the spectral lines.