Question

suppose you were given the exact same setup described in Section B, except that a different grating with fewer grooves/cm was used. how would you expect this to affect the location of the first-order spot?

Answer 1

A grating with fewer grooves/cm means the groove spacing is higher now.

The minimum angle for constructive interference decreases according to the given equation if the same light is used for experimentation by the experimenter. The reason is that the wavelength and the diffraction order are set. Sin(theta) decreases since the distance between the groove is increased. This reduces Theta's value (minimum).

When theta reduces, the first position in order is similar to the zero-order limit.