The refractive index of glass with respect to water is `9/8`. If the velocity and wavelength of light in water are `2.25 xx 10^(8) ms^(-1)` and 5400 `overset(o)(A)`, then the velcoity and wavelength of light in glass are

Options

A. `2xx10^(8)ms^(-1),4800overset(o)(A)`
B. `1xx10^(8)ms^(-1),6075overset(o)(A)`
C. `2xx10^(8)ms^(-1),6075overset(o)(A)`
D. `1xx10^(8)ms^(-1),4800overset(o)(A)`

Explanation

To solve the problem step by step, we will use the relationships between the refractive index, velocity, and wavelength of light in different media.

### Step 1: Understand the given data
- Refractive index of glass with respect to water (μ_g/w) = 9/8
- Velocity of light in water (V_w) = 2.25 × 10^8 m/s
- Wavelength of light in water (λ_w) = 5400 Å (1 Å = 10^-10 m)

### Step 2: Use the relationship of refractive index
The refractive index (μ) is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in the medium. For two media, we can express it as:
\[ \frac{\mu_{glass}}{\mu_{water}} = \frac{V_{water}}{V_{glass}} = \frac{\lambda_{water}}{\lambda_{glass}} \]

### Step 3: Calculate the velocity of light in glass (V_g)
From the relationship:
\[ \frac{\mu_{glass}}{\mu_{water}} = \frac{V_{water}}{V_{glass}} \]
We can rearrange this to find the velocity of light in glass:
\[ V_{glass} = V_{water} \times \frac{\mu_{water}}{\mu_{glass}} \]

Given that:
\[ \frac{\mu_{glass}}{\mu_{water}} = \frac{9}{8} \implies \frac{\mu_{water}}{\mu_{glass}} = \frac{8}{9} \]

Now substituting the values:
\[ V_{glass} = 2.25 \times 10^8 \times \frac{8}{9} \]

Calculating this:
\[ V_{glass} = 2.25 \times 10^8 \times \frac{8}{9} = 2.00 \times 10^8 \, \text{m/s} \]

### Step 4: Calculate the wavelength of light in glass (λ_g)
Using the relationship:
\[ \frac{\mu_{glass}}{\mu_{water}} = \frac{\lambda_{water}}{\lambda_{glass}} \]
We can rearrange this to find the wavelength in glass:
\[ \lambda_{glass} = \lambda_{water} \times \frac{\mu_{water}}{\mu_{glass}} \]

Substituting the values:
\[ \lambda_{glass} = 5400 \, \text{Å} \times \frac{8}{9} \]

Calculating this:
\[ \lambda_{glass} = 5400 \times \frac{8}{9} = 4800 \, \text{Å} \]

### Final Results
- Velocity of light in glass (V_g) = 2.00 × 10^8 m/s
- Wavelength of light in glass (λ_g) = 4800 Å

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