Question

Write the reason behind the shining of diamond.

Hint:

The brilliance of a diamond depends on three optical properties: refractive index (determines light bending), critical angle (determines TIR condition), and dispersion (creates colorful fire). All three are exceptionally high in diamonds compared to other gemstones.

Answer 1

The shining of a diamond is primarily due to a phenomenon called Total Internal Reflection (TIR) combined with its high refractive index and proper cutting.
Main Reasons for Diamond's Shining: \vspace{0.3cm} 
1. Total Internal Reflection (TIR): 

This is the most important reason for diamond's brilliance. 
When light enters a diamond, it strikes the internal faces at angles greater than the critical angle. 
Instead of passing through, the light is completely reflected back inside the diamond. 
This multiple internal reflection causes the light to bounce around before finally exiting, creating maximum brilliance. 

2. High Refractive Index: 

Diamond has an exceptionally high refractive index of 
2.42 (compared to glass ~1.5). 
Refractive index determines how much light bends when entering the material. 
Higher refractive index means: 

More bending of light 
Smaller critical angle 
Greater chance of total internal reflection 


3. Small Critical Angle: 

The critical angle for diamond is approximately 
24.4°. 
This is very small compared to other transparent materials (glass critical angle ~42°). 
Because of this small critical angle, most light rays entering the diamond strike the internal surfaces at angles greater than 24.4°, causing total internal reflection. 

4. Proper Cutting and Faceting: 

Diamonds are cut with multiple flat surfaces called facets (typically 58 facets in a brilliant cut). 
The precise angles and arrangement of facets are designed to: 

Maximize total internal reflection 
Allow light to enter easily 
Trap light inside through multiple reflections 
Release light in specific directions to create sparkle 

Poorly cut diamonds lose light through the bottom (called ""light leakage"") and appear dull. 

5. Dispersion (Fire): 

Diamond has high dispersion, meaning it splits white light into its component colors (like a prism). 
This creates the colorful flashes (called ""fire"") that add to diamond's brilliance. 
Dispersion in diamond is 0.044, higher than most gemstones. 
Mathematical Explanation: \vspace{0.3cm} Critical Angle Formula: \[ \sin C = \frac{1}{\mu} \] where: 

$C$ = critical angle 
$\mu$ = refractive index of diamond relative to air 
For diamond ($\mu = 2.42$): \[ \sin C = \frac{1}{2.42} = 0.413 \] \[ C = \sin^{-1}(0.413) \approx 24.4° \] Since the critical angle is small, most light rays entering the diamond hit the internal surface at angles >24.4°, causing total internal reflection. 

Comparison with Other Materials:
 

Path of Light in a Diamond: 

 

Factors Affecting Diamond's Shine: 

Cut Quality: Determines how well light is reflected internally 
Clarity: Inclusions can scatter light and reduce brilliance 
Polish: Smooth surfaces ensure proper reflection 
Symmetry: Precise facet alignment is crucial 
Final Answer: \[ \boxed{\text{Diamond shines due to Total Internal Reflection (TIR) caused by its high refractive index (2.42) and small critical angle (24.4°), combined with proper cutting/faceting that traps light inside through multiple reflections.}} \]