Question

In a spectrum obtained with a prism which color is deviated maximum?
$(A)$ Violet
$(B)$Red
$(C)$Green
$(D)$Orange

Answer 1

Hint : Use the velocity of light in the medium formula, the refractive index of the medium in terms of velocities of light, and the refractive index of the material of prism in the minimum angle of deviation of light. Drive the relation using these formulas the relation between the minimum angle of deviation of color light and wavelength of light.

Complete step-by-step solution:
The velocity \[v\] is given by,
\[v = n\lambda .........\left( 1 \right)\]
Here, \[n\] is the frequency of the light
\[\lambda \]is the wavelength of the light
The refractive index of \[\mu \] a medium is,
\[\mu = \dfrac{c}{v}.........\left( 2 \right)\]
Here, \[c\]is the velocity of the light in a vacuum
\[v\]is the velocity of the light in the medium
The refractive index of the material of prism is,
\[\mu = \dfrac{{\sin \left( {\dfrac{{A + {\delta _m}}}{2}} \right)}}{{\sin \dfrac{A}{2}}}.......\left( 3 \right)\]
Here, \[A\]is the angle of the prism
\[{\delta _m}\]is the minimum angle of deviation.
The light passes through the prism, it splits into its seven constituent colors because of the dispersion of white light. The seven colors are violet, indigo, blue, green, orange, yellow, and red. The angle of minimum deviation for all the seven colors is different because these colors under different extents of refraction by the prism, all have different velocities. From equation (3), it can be concluded the angle of minimum deviation will be maximum for the color with maximum refraction as the angle of the minimum deviation is directly proportional to the refractive index of the prism.
\[\mu \propto {\delta _m}.........\left( 4 \right)\]
The equation (\[2\]) shows the refractive index of the material of the prism is inversely proportional to the speed of the light in the prism as the speed of light in a vacuum is constant.
\[\mu \propto \dfrac{1}{v}............\left( 5 \right)\]
From the equation,\[\left( 1 \right)\]we can conclude that the velocity is directly proportional to the wavelength of the light.
\[v \propto \lambda ........\left( 6 \right)\]
From the relation\[\left( 4 \right),\left( 5 \right),\left( 6 \right)\], we can write the relation
\[{\delta _m} \propto \dfrac{1}{\lambda }\]
The wavelength of the light is inversely proportional to the angle of minimum deviation. The angle of minimum deviation will be greater than the color of light having a minimum wavelength. So the violet color is the violet color of light that has a minimum wavelength. The Violet color of light has maximum deviation when the light passes through the prism.
Hence, the answer is Violet.

Note:The violet color among other colors has maximum deviation when passed through a prism. The deriving the relation between minimum angle deviation and wavelength of the light. The violet color has the least wavelength. Therefore when it travels from one medium to another medium, it has the maximum value of the angle of incidence, and hence the violet color will deviate the most.