Question

Which color shows maximum deviation when light is passed through prism?
A. violet
B. red
C. yellow
D. blue

Answer 1

Hint: Use the formulae for the velocity of light in a medium, the refractive index of medium in terms of velocities of light and the refractive index of the material of the prism in terms of minimum angle of deviation of the light. Using these three formulae, derive the relation between the minimum angle of deviation of the color of light and wavelength of light.

Formulae used:
The velocity \[v\] is given by
\[v = n\lambda \] …… (1)
Here, \[n\] is the frequency of the light and \[\lambda \] is the wavelength of the light.
The refractive index \[\mu \] of a medium is given by
\[\mu = \dfrac{c}{v}\] …… (2)
Here, \[c\] is the velocity of the light in vacuum and \[v\] is the velocity of the light in the medium.
The refractive index of material of prism is given by
\[\mu = \dfrac{{\sin \left( {\dfrac{{A + {\delta _m}}}{2}} \right)}}{{\sin \dfrac{A}{2}}}\] …… (3)
Here, \[A\] is the angle of prism and \[{\delta _m}\] is the minimum angle of deviation.

Complete step by step answer:
When a white light passes through a prism, it splits into its seven constituent colors because of dispersion of white light.These colors are violet, indigo, blue, green, yellow, orange and red.The angle of minimum deviation for all these seven colors are different because these colors undergo different extents of refraction by the prism as they all have different velocities.From equation (3), it can be concluded that the angle of minimum deviation will be maximum for the color which undergoes maximum refraction as the angle of minimum deviation is directly proportional to the refractive index of the material of the prism.
\[\mu \propto {\delta _m}\] …… (4)
But equation (2) shows that 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 vacuum is constant.
\[\mu \propto \dfrac{1}{v}\] …… (5)
From equation (1), we can conclude that the velocity is directly proportional to the wavelength of the light.
\[v \propto \lambda \] …… (6)
From the relations (4), (5) and (6), we can write the relation
\[{\delta _m} \propto \dfrac{1}{\lambda }\]
Hence, the angle of minimum deviation is inversely proportional to the wavelength of the light.Therefore, the angel of minimum deviation will be greater for the color of light having minimum wavelength.Among the given options, the violet color of light has the minimum wavelength. Therefore, the violet color of light undergoes maximum deviation when the light passes through the prism.

Hence, the correct option is A.

Note: The students should always remember that the violet color amongst all the seven colors of light have maximum deviation when passes through prism always and not for the present question.The students should be careful while deriving the relation between the minimum angle of deviation and wavelength of the light. If this relation is not derived correctly, the answer will be incorrect.