Question 29: Units , Dimensions and Error Analysis

Question

Suppose refractive index $$\alpha$$ is given as $$ \alpha  = A + {B \over {{\lambda ^2}}}$$, where A and B are constants and $$\lambda$$ is wavelength, then dimensions of B are same as that of

Accepted Answer

Refractive index, $$ \alpha  = A + {B \over {{\lambda ^2}}}$$
According to principle of homogeneity,
Dimension of $${B \over {{\lambda ^2}}} = $$ Dimension of $$\alpha$$
$$ \Rightarrow [B] = [ \propto ][{\lambda ^2}]$$
$$ = [{M^0}{L^0}{T^0}][{L^2}]$$
$$ = [{L^2}]$$
= Dimension of area

Answer

wavelength

Answer

volume

Answer

pressure

Answer

area

Units , Dimensions and Error Analysis

Suppose refractive index $\alpha is given as \alpha = A + {B \over {{\lambda ^2}}}, where A and B are constants and \lambda$ is wavelength, then dimensions of B are same as that of

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