Final answer:
A gem must be cut to specific dimensions to maximize light reflection and refraction, taking advantage of the gem's critical angle and high index of refraction compared to air. This enhances the gem's sparkle and aesthetic value.
Step-by-step explanation:
A gem must be cut to specific dimensions in order to maximize its ability to reflect and refract light, creating the characteristic sparkle and brilliance. The cutting process involves creating facets at precise angles which are designed to take advantage of the gem's critical angle—the minimum angle of incidence above which light is totally reflected within the gem and does not pass through it. Because the index of refraction of a diamond is very high compared to air, the critical angle is small, which means most light entering a diamond will undergo total internal reflection.
The facets of a gem like a diamond are strategically placed so that light can exit the gem in very specific ways, concentrating the light and enhancing its sparkle. If a gem is not cut to these specific dimensions, it will not interact with light in the optimal way, and its appearance will suffer as a result. Hence, meticulously cutting a gem to achieve the desired optical effects is crucial for revealing its full beauty and value.