Final answer:
The line spectrum observed using a spectroscope will only change in size when the distance between the prism and the screen is adjusted, without altering the spectral information; however, when using a diffraction grating, the distances between lines can become more pronounced.
Step-by-step explanation:
If we consider the question of whether the line spectrum observed on a screen using a spectroscope would change if the distance between the prism and the screen changed, the answer depends on the context of the experiment. When light enters a prism, it is dispersed into its constituent wavelengths or colors, producing a spectrum. This is similar to the dispersion of light by raindrops forming a rainbow. A spectroscope uses a prism or diffraction grating to disperse light into a spectrum, which is then projected onto a screen.
When using a prism, the position of the spectral lines relative to each other doesn't change with distance because the dispersion is a property of the material's index of refraction and the wavelength of light. However, the size of the spectrum on the screen would change if the screen is moved further from the prism; it would spread out more and become larger. On the other hand, if a diffraction grating is used, not only would the size of the spectrum change but the distances between the lines could also become more pronounced, allowing for greater resolution and the possibility to observe more detail within the spectrum.
It's important to note that while the color pattern stretches with distance, the actual spectral information (the specific wavelengths present) does not change, only how spread out the colors appear on the screen. If the screen is moved closer to the prism, the spectrum would shrink but still contain the same spectral information.