What is the basic physical reason for the extraordinary sparkle and brilliance of a suitably cut diamond?

Introduction / Context:
Diamonds are famous for their intense sparkle and brilliant flashes of light when cut and polished properly. Jewellers take advantage of the optical properties of diamond to design cuts that maximise this effect. From the point of view of physics, this brilliance can be explained by the way light behaves inside the stone. This question focuses on which fundamental property of diamond is mainly responsible for its extraordinary sparkle.

Given Data / Assumptions:

• We are considering a well cut, transparent diamond used in jewellery.
• Light enters the diamond from air and undergoes refraction and reflection inside.
• The options mention properties such as cleavage planes, transparency, refractive index, and hardness.
• We assume normal viewing conditions in air, with visible light.

Concept / Approach:
The key optical property here is the refractive index of diamond, which is very high compared to many other transparent materials. A high refractive index means that light slows down significantly inside the material and bends strongly at the interface. Because of this, the critical angle for total internal reflection inside diamond is small. Light entering the diamond is repeatedly totally internally reflected from the internal surfaces instead of escaping. Combined with dispersion, which separates colours, this leads to many bright flashes of light emerging from different facets, creating the well known sparkle. Thus, the very high refractive index is the fundamental reason for diamond brilliance.

Step-by-Step Solution:
Step 1: Recall that diamond has a refractive index of about 2.4, which is much higher than that of glass, which is around 1.5. Step 2: A higher refractive index leads to a smaller critical angle for total internal reflection at the diamond air interface. Step 3: When light enters the diamond, it is refracted and then strikes the internal surfaces at angles greater than the critical angle. Step 4: Under these conditions, total internal reflection occurs many times, trapping light inside and directing it through different facets. Step 5: Carefully chosen cut angles maximise the number of internal reflections and the amount of light that eventually emerges from the top of the stone. Step 6: Therefore, the key physical reason for the extraordinary sparkle is the very high refractive index of diamond.

Verification / Alternative check:
If a diamond is placed in a liquid whose refractive index is close to that of diamond, such as certain oils, its brilliance almost disappears because the contrast in refractive index is reduced and total internal reflection is lost. Similarly, glass with lower refractive index does not show the same level of sparkle even when cut in similar shapes. These observations confirm that refractive index, and not simply hardness or transparency, is the dominant factor behind the characteristic brilliance. Professional gem cutting is designed specifically around the optical behaviour that comes from the high refractive index.

Why Other Options Are Wrong:
Well defined cleavage planes: These refer to how the crystal breaks along certain directions and are important for cutting, but they do not directly cause sparkle.
Very high transparency only: Transparency allows light to pass through, but many transparent materials are not particularly brilliant; refractive index and internal reflection are more important.
Extreme hardness: Hardness makes diamond durable and resistant to scratching, which is valuable for jewellery, but it does not explain the optical brilliance.

Common Pitfalls:
A common mistake is to think that hardness or simple transparency is responsible for sparkle. Another confusion is to overlook the role of total internal reflection and assume that any highly polished transparent object will show the same effect. In reality, it is the combination of high refractive index and appropriate cutting that creates the unique brilliance of diamond. Remember that refractive index governs how light bends and reflects, which is central to this phenomenon.

Final Answer:
The basic physical reason for the extraordinary sparkle of a cut diamond is that it has a very high refractive index.