
According to Cauchy, the Refractive index is
A. Directly proportional to the wavelength of light
B. Directly proportional to the square of the wavelength of light
C. Inversely proportional to the wavelength of light
D. Inversely proportional to the square of the wavelength of light
Answer
497.4k+ views
1 likes
Hint: An empirical/dispersion relationship between the wavelength of the light and the refractive index for a particular transparent material is the Cauchy’s transmission equation. The empirical coefficients of Cauchy’s equation represent the nature of the material.
Formula used:
Complete step-by-step solution:
The Cauchy’s equation is given by,
Where n is the refractive index, is the wavelength and A, B, C, ….. are the coefficients coated for as the vacuum wavelengths (empirical coefficients).
As the wavelength is in terms of nanometers, the wavelengths with the higher powers can be omitted.
So, the equation reduces as follows.
The refractive index is inversely proportional to the square of the wavelength of light.
As, according to Cauchy’s equation, the refractive index is inversely proportional to the square of the wavelength of light, thus, option (D) is correct.
Additional information:
This Cauchy’s equation is only valid for the regions of the normal dispersion in the visible wavelength.
The parallel beams of light incident on a lens will bend more towards the axis in the case blue light when compared to the red light, as hence .
The red light gets less dispersed than the violet light because the refractive index is inversely proportional to the wavelength of the light, as, the wavelength of violet light is less than that of the red light.
Note: The things to be on your finger-tips for further information on solving these types of problems are: There are different Cauchy’s equations: They are: Cauchy’s functional equation, Cauchy momentum equation, and Cauchy’s equation in optics. All these belong to different concepts.
Formula used:
Complete step-by-step solution:
The Cauchy’s equation is given by,
Where n is the refractive index,
As the wavelength is in terms of nanometers, the wavelengths with the higher powers can be omitted.
So, the equation reduces as follows.
The refractive index is inversely proportional to the square of the wavelength of light.
As, according to Cauchy’s equation, the refractive index is inversely proportional to the square of the wavelength of light, thus, option (D) is correct.
Additional information:
This Cauchy’s equation is only valid for the regions of the normal dispersion in the visible wavelength.
The parallel beams of light incident on a lens will bend more towards the axis in the case blue light when compared to the red light, as
The red light gets less dispersed than the violet light because the refractive index is inversely proportional to the wavelength of the light, as, the wavelength of violet light is less than that of the red light.
Note: The things to be on your finger-tips for further information on solving these types of problems are: There are different Cauchy’s equations: They are: Cauchy’s functional equation, Cauchy momentum equation, and Cauchy’s equation in optics. All these belong to different concepts.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?

Why should a magnesium ribbon be cleaned before burning class 12 chemistry CBSE

A renewable exhaustible natural resources is A Coal class 12 biology CBSE

Megasporangium is equivalent to a Embryo sac b Fruit class 12 biology CBSE

What is Zeises salt and ferrocene Explain with str class 12 chemistry CBSE

How to calculate power in series and parallel circ class 12 physics CBSE
