The refractive index of diamond is 2.42. What is the meaning of this statement?
The statement means that the ratio of the speed of light in air to the speed of light in diamond is equal to 2.42. This can be expressed as: n_m = c/v = 2.42, where c is the speed of light in air and v is the speed of light in diamond.
This indicates that light travels slower in diamond compared to air. Since the refractive index of diamond (2.42) is higher than other media like water (1.33) or glass (1.52), diamond is optically denser than these materials. The higher refractive index means light bends significantly when entering diamond from air.
Explanation
The textbook explains refractive index as the ratio of speed of light in air to speed of light in the medium (Equation 9.7). Using the example of water (n_w = 1.33), it clarifies that this means the ratio of speeds equals the refractive index value. Applying this to diamond, n = 2.42 means light travels 2.42 times slower in diamond than in air. The textbook also notes that higher refractive index indicates optical density.
Solution Steps
Step 1: Identify the formula for refractive index from context: n_m = c/v
Step 2: Apply to diamond: n_diamond = Speed of light in air / Speed of light in diamond = 2.42
Step 3: Interpret: Light travels 2.42 times slower in diamond than in air