Question

Suppose refractive index μ is given as \[\mu = A + \dfrac{B}{{{\lambda ^2}}}\]where A and B are constants and is wavelength, then dimensions of B are same as that of:
A. Wavelength
B. Volume
C. Pressure
D. Area

Answer 1

Hint: Use the logic that has no dimension.

Complete step by step answer:
We know that,
\[\mu \]=(the velocity of light in vacuum)/(velocity of light in medium)
Since, we know that has no dimension, from the given equation,
\[\mu = A + \dfrac{B}{{{\lambda ^2}}}\]
The dimension analysis for:
\[\mu \]is $\left[ {{M^0}{L^0}{I^0}{T^0}} \right]$
Where, M is mass,
                L is length,
                T is time
The refractive index is a dimensionless quantity.
\[\lambda \] is$\left[ {{M^0}{L^1}{T^0}} \right]$
Where, M is mass,
                L is length,
                T is time
We can understand that B/ 2 also has no dimension. Since the dimension of 2 is cm², the dimension of B will also be cm², that is, the dimensions of area.
The dimensional formula of area is:
\[\left[ {{M^0}{L^2}{T^0}} \right]\]
Where, M is mass,
                L is length,
                T is time
Therefore, we can conclude that option (D) is our correct option.

Additional information: The direction of propagation of an incident oblique ray of light, entering a different medium changes at the interface of both media, and this phenomenon is called refraction of light.
We can explain the phenomenon of Refraction as the change in direction of propagation of light when the medium in which the light is traveling changes. Refraction of light can be explained using the theory of conservation of momentum and theory of conservation of energy. Since the medium of travel of light changes, the wave's phase velocity changes but its frequency remains unchanged. There are also two laws of refraction also known as Snell's Laws. They are-
(A) The refracted ray, the incident ray, and the normal at the point of incidence all lie on the same plane.
(B)The ratio of the sine of the angle of refraction(r) to the sine of the angle of incidence is constant for both of the given mediums. The constant is known as the refractive index of the first media with respect to the second.

Note: Remember that A is also non-dimensional since the entire right side is non-dimensional.