The refractive index of glass with respect to water is `1.125` . If the speed of light in water is `2.25 xx 10^(8) ms^(-1)` , what is the speed of light in glass ?

Answer

To find the speed of light in glass, we can use the relationship between the refractive index, the speed of light in a medium, and the speed of light in a vacuum. The refractive index (n) of a medium with respect to another medium can be defined as:

\[ n = \frac{c_1}{c_2} \]

where:
- \( c_1 \) is the speed of light in the first medium (water in this case),
- \( c_2 \) is the speed of light in the second medium (glass in this case).

Given:
- The refractive index of glass with respect to water, \( n_{glass/water} = 1.125 \)
- The speed of light in water, \( c_{water} = 2.25 \times 10^8 \, \text{m/s} \)

We need to find the speed of light in glass, \( c_{glass} \).

### Step 1: Write the equation for refractive index
Using the definition of refractive index:

\[ n_{glass/water} = \frac{c_{water}}{c_{glass}} \]

### Step 2: Rearrange the equation to solve for \( c_{glass} \)
Rearranging the equation gives us:

\[ c_{glass} = \frac{c_{water}}{n_{glass/water}} \]

### Step 3: Substitute the known values
Now we can substitute the known values into the equation:

\[ c_{glass} = \frac{2.25 \times 10^8 \, \text{m/s}}{1.125} \]

### Step 4: Perform the calculation
Calculating the above expression:

\[ c_{glass} = 2.25 \times 10^8 \div 1.125 \]

Calculating this gives:

\[ c_{glass} = 2.0 \times 10^8 \, \text{m/s} \]

### Final Answer
The speed of light in glass is \( 2.0 \times 10^8 \, \text{m/s} \).

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