Refractive index mu is given as `mu=A+B/lambda^2,` where A and B are constants and lambda is wavelength, then dimensions of B are same as that of

Options

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

Explanation

To determine the dimensions of the constant \( B \) in the equation for the refractive index \( \mu \), we start with the given equation:

\[ \mu = A + \frac{B}{\lambda^2} \]

### Step 1: Understand the dimensions of the refractive index \( \mu \)

The refractive index \( \mu \) is defined as the ratio of the speed of light in vacuum to the speed of light in a medium. Since it is a ratio of two speeds, it is dimensionless. Therefore, we can express its dimensions as:

\[ [\mu] = M^0 L^0 T^0 \]

### Step 2: Analyze the term \( \frac{B}{\lambda^2} \)

In the equation, \( \mu \) is equal to \( A + \frac{B}{\lambda^2} \). Since \( \mu \) is dimensionless, the term \( \frac{B}{\lambda^2} \) must also be dimensionless. This implies:

\[ \left[\frac{B}{\lambda^2}\right] = M^0 L^0 T^0 \]

### Step 3: Determine the dimensions of \( \lambda \)

The wavelength \( \lambda \) is a measure of length, so its dimensions are:

\[ [\lambda] = L \]

### Step 4: Find the dimensions of \( \lambda^2 \)

Since \( \lambda \) has dimensions of length, the dimensions of \( \lambda^2 \) are:

\[ [\lambda^2] = L^2 \]

### Step 5: Set up the equation for dimensions of \( B \)

From the previous steps, we know that:

\[ \left[\frac{B}{\lambda^2}\right] = [B] \cdot [\lambda^{-2}] = [B] \cdot L^{-2} \]

Since \( \left[\frac{B}{\lambda^2}\right] \) is dimensionless, we can write:

\[ [B] \cdot L^{-2} = M^0 L^0 T^0 \]

### Step 6: Solve for the dimensions of \( B \)

To make the left side dimensionless, \( [B] \) must have dimensions that cancel out \( L^{-2} \):

\[ [B] = L^2 \]

### Conclusion

Thus, the dimensions of \( B \) are the same as those of \( \lambda^2 \), which is:

\[ [B] = L^2 \]