Q.10
The refractive index of diamond is 2.419. If the speed of light in vacuum is 3 · 10⁸ m s⁻¹, then the speed of light in diamond is
(A) 1.240 · 10⁸ m s⁻¹
(B) 1.352 · 10⁸ m s⁻¹
(C) 1.521 · 10⁸ m s⁻¹
(D) 2.433 · 10⁸ m s⁻¹
Introduction to Speed of Light in Diamond
Discover how to calculate the speed of light in diamond using its refractive index of 2.419 and vacuum speed of \( 3 \times 10^8 \) m/s. This essential physics concept appears in competitive exams like CSIR NET, explaining light’s behavior in dense media like diamond .
Calculation Steps
The speed of light in diamond is calculated using the refractive index formula \( n = \frac{c}{v} \), where \( c = 3 \times 10^8 \) m/s is the speed in vacuum and \( n = 2.419 \), so \( v = \frac{c}{n} = 1.240 \times 10^8 \) m/s. This matches option (A) .
The refractive index relates speeds directly: \( v = \frac{3 \times 10^8}{2.419} \). Dividing yields approximately 124,055,564 m/s, or \( 1.240 \times 10^8 \) m/s when rounded to match the options .
Option Analysis
| Option | Value | Analysis |
|---|---|---|
| (A) | \( 1.240 \times 10^8 \) m/s | Correct, as \( \frac{3 \times 10^8}{1.240 \times 10^8} = 2.419 \) . |
| (B) | \( 1.352 \times 10^8 \) m/s | Incorrect, gives \( n = 2.219 \), too low for diamond . |
| (C) | \( 1.521 \times 10^8 \) m/s | Incorrect, gives \( n = 1.972 \), typical for glass, not diamond . |
| (D) | \( 2.433 \times 10^8 \) m/s | Incorrect, gives \( n = 1.233 \), closer to air than diamond . |
Refractive Index Formula Explained
Refractive index \( n \) is \( n = \frac{c}{v} \), where \( c \) is vacuum speed and \( v \) is medium speed. For diamond, rearrange to \( v = \frac{c}{n} = \frac{3 \times 10^8}{2.419} = 1.240 \times 10^8 \) m/s. Diamond’s high \( n \) (2.417-2.419) slows light significantly compared to vacuum .
Why Diamond Refractive Index Matters
Diamond’s \( n = 2.419 \) causes brilliance via total internal reflection. Light speed drops to about 41.3% of vacuum value, enabling sparkle in jewelry. This property distinguishes it from gems like sapphire (\( n \approx 1.76 \)) .
MCQ Solution and Common Errors
In the query MCQ, option (A) matches exactly. Errors occur by inverting formula (yielding speeds > \( c \)) or misrounding. Always verify: higher \( n \) means lower \( v \) .
Exam Tips for Refractive Index Problems
- Memorize \( c = 3 \times 10^8 \) m/s.
- Practice: glass \( n = 1.5 \), \( v = 2 \times 10^8 \) m/s.
- Use calculator for precision in exams.
