(a) Would the pattern change if you were to use a shorter wavelength of light? Clearly state what change(s) would occur (if any) and briefly explain why.

(b) The apparatus is surrounded by air. Would the pattern change if it were immersed in water instead? Clearly state what change(s) would occur (if any), and briefly explain why.

(a) If you were to use a shorter wavelength of light, the pattern would indeed change. This is because the pattern formed by a diffraction grating depends on the wavelength of light used. A diffraction grating consists of closely spaced parallel slits or rulings, which causes the incident light to diffract and create interference patterns.

The pattern of bright and dark fringes produced by a diffraction grating is given by the equation:

sinθ = mλ/d

Where:
- sinθ is the angle between the diffracted light and the normal to the grating surface,
- m is the order of the bright fringe,
- λ is the wavelength of the incident light, and
- d is the separation between the slits or rulings on the grating.

In this equation, we can see that the pattern is directly dependent on the wavelength, represented by λ. Therefore, if a shorter wavelength of light is used, the value of λ will change, which will eventually lead to a change in the pattern. Specifically, the distance between the fringes would decrease, resulting in a denser pattern of fringes.

(b) If the apparatus were immersed in water instead of being surrounded by air, the pattern would also change. This is because the refractive index of water is different from that of air. The refractive index, denoted by n, determines how much the speed of light changes when passing from one medium to another.

When light passes from air into water or any other medium, it changes direction due to the change in speed. This phenomenon is known as refraction. The change in direction of light during refraction can affect the path of the diffracted light.

In the case of a diffraction grating immersed in water, the change in refractive index would cause the angle at which the light diffracts to be different. Consequently, the pattern of bright and dark fringes observed would be altered. The specific change in the pattern would depend on the difference in refractive indices between water and air, as well as the wavelength of light used.