MHT CET · Physics · Units and Dimensions
The refractive index of the medium is \(\mu=\mathrm{A}+\frac{\mathrm{B}}{\lambda^{2}}\), where \(\mathrm{A}\) and \(\mathrm{B}\) are constants and \(\lambda\) is the wavelength of light. The dimensions of \(B\) are same as that of
- A Velocitv.
- B area.
- C wavelength.
- D Volume.
Answer & Solution
Correct Answer
(B) area.
Step-by-step Solution
Detailed explanation
\(\mu=\mathrm{A}+\frac{\mathrm{B}}{\lambda^{2}}\). Equating dimensions give
\(\frac{\mathrm{B}}{\lambda^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\) \(\Rightarrow \mathrm{B}=\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0} \rightarrow\) same as dimension of area.
\(\frac{\mathrm{B}}{\lambda^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\) \(\Rightarrow \mathrm{B}=\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0} \rightarrow\) same as dimension of area.
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