The refractive index of a medium is given by `mu=A+(B)/(lambda^(2))` where A and B are constants and `lambda` is the wavelength of light.
Then the dimensions of B are the same as that of

Options

A. Wavelength
B. Area
C. Volume
D. Velocity

Explanation

To find the dimensions of the constant \( B \) in the equation for the refractive index \( \mu = A + \frac{B}{\lambda^2} \), we will follow these steps:

### Step 1: Understand the equation
The equation given is:
\[ \mu = A + \frac{B}{\lambda^2} \]
where \( \mu \) is the refractive index, \( A \) and \( B \) are constants, and \( \lambda \) is the wavelength of light.

### Step 2: Identify the dimensions of \( \mu \)
The refractive index \( \mu \) is a dimensionless quantity. Therefore, we have:
\[ [\mu] = 1 \]

### Step 3: Analyze the term \( \frac{B}{\lambda^2} \)
For the equation to be dimensionally consistent, the dimensions of \( A \) and \( \frac{B}{\lambda^2} \) must also be dimensionless. Since \( A \) is a constant, we can focus on the term \( \frac{B}{\lambda^2} \).

### Step 4: Write the dimensions of \( \lambda \)
The wavelength \( \lambda \) has the dimension of length:
\[ [\lambda] = L \]
Thus, the dimensions of \( \lambda^2 \) are:
\[ [\lambda^2] = L^2 \]

### Step 5: Set up the dimensional equation
Since \( \frac{B}{\lambda^2} \) must be dimensionless, we can express this as:
\[ \frac{[B]}{[\lambda^2]} = 1 \]
This implies:
\[ [B] = [\lambda^2] \]

### Step 6: Substitute the dimensions of \( \lambda^2 \)
From the previous step, we know:
\[ [B] = L^2 \]

### Step 7: Conclusion
The dimensions of \( B \) are the same as the dimensions of area, which is \( L^2 \).

### Final Answer
The dimensions of \( B \) are the same as that of area.

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