Question

The refractive index of a medium is \( \mu = A + \dfrac{B}{\lambda^2} \), where \( A \) and \( B \) are constants and \( \lambda \) is the wavelength of light. The dimensions of \( B \) are same as that of

• A. velocity
• B. area
• C. wavelength
• D. volume

Hint:

Always ensure dimensional homogeneity when physical quantities are added or subtracted.

Answer 1

The Correct Option is B

Step 1: Analyze dimensions of refractive index.
Refractive index \( \mu \) is a dimensionless quantity.
Step 2: Write dimensional consistency.
Since \( A \) is added to \( \dfrac{B}{\lambda^2} \), both terms must be dimensionless.
Step 3: Find dimensions of \( B \).
\[ \frac{B}{\lambda^2} = \text{dimensionless} \Rightarrow [B] = [\lambda^2] \]
Step 4: Conclusion.
The dimensions of \( B \) are same as area.