The wavelength of light in vacuum is `6000 A^(@)` and in a medium it is `4000 A^(@)` The refractive index of the medium is:

Options

A. `2.4`
B. `1.5`
C. `1.2`
D. `0.67`

Explanation

To find the refractive index of the medium given the wavelengths of light in vacuum and in the medium, we can follow these steps:

### Step 1: Understand the formula for 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 the medium (v). This can also be expressed in terms of the wavelengths of light in vacuum (λ_v) and in the medium (λ_m):
\[ n = \frac{c}{v} = \frac{\lambda_v}{\lambda_m} \]

### Step 2: Identify the given values
From the problem, we have:
- Wavelength in vacuum (λ_v) = 6000 Å (angstroms)
- Wavelength in medium (λ_m) = 4000 Å (angstroms)

### Step 3: Substitute the values into the formula
Now we can substitute the values into the refractive index formula:
\[ n = \frac{\lambda_v}{\lambda_m} = \frac{6000 \, \text{Å}}{4000 \, \text{Å}} \]

### Step 4: Simplify the fraction
Now, we simplify the fraction:
\[ n = \frac{6000}{4000} = \frac{6}{4} = \frac{3}{2} \]

### Step 5: Calculate the numerical value
Calculating the numerical value gives:
\[ n = 1.5 \]

### Step 6: Conclusion
Thus, the refractive index of the medium is:
\[ n = 1.5 \]

### Final Answer
The correct option is **1.5**.

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