The velocity of light in diamond, glass and water decreases in the following order

Options

A. watergt glassgt diamond
B. diamondgt glassgt water
C. diamondgt watergt glass
D. watergt diamondgt glass

Explanation

To determine the order of the velocity of light in diamond, glass, and water, we need to understand the relationship between the speed of light in a medium and its refractive index.

### Step-by-Step Solution:

1. **Understanding Refractive Index**:
The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v):
\[ n = \frac{c}{v} \]
From this, we can see that the speed of light in a medium is inversely proportional to its refractive index:
\[ v = \frac{c}{n} \]

2. **Refractive Indices of the Media**:
- Refractive index of water (n_water) = \( \frac{4}{3} \) ≈ 1.33
- Refractive index of glass (n_glass) = \( \frac{3}{2} \) = 1.5
- Refractive index of diamond (n_diamond) = 2.4

3. **Calculating the Speed of Light in Each Medium**:
- For water:
\[ v_{water} = \frac{c}{n_{water}} = \frac{c}{\frac{4}{3}} = \frac{3c}{4} \]
- For glass:
\[ v_{glass} = \frac{c}{n_{glass}} = \frac{c}{\frac{3}{2}} = \frac{2c}{3} \]
- For diamond:
\[ v_{diamond} = \frac{c}{n_{diamond}} = \frac{c}{2.4} \approx \frac{5c}{12} \]

4. **Comparing the Speeds**:
To compare the speeds, we can express them as fractions of c:
- \( v_{water} = \frac{3c}{4} \)
- \( v_{glass} = \frac{2c}{3} \)
- \( v_{diamond} \approx \frac{5c}{12} \)

Now we can convert these to a common denominator to compare:
- \( v_{water} = \frac{9c}{12} \)
- \( v_{glass} = \frac{8c}{12} \)
- \( v_{diamond} = \frac{5c}{12} \)

5. **Ordering the Velocities**:
From the above calculations, we can see that:
\[ v_{water} > v_{glass} > v_{diamond} \]
Therefore, the order of the velocity of light in these media is:
\[ \text{Water} > \text{Glass} > \text{Diamond} \]

### Final Answer:
The velocity of light in diamond, glass, and water decreases in the following order:
\[ \text{Water} > \text{Glass} > \text{Diamond} \]