Answer
Verified
315k+ views
Hint:The breaking of white light into its constituent colours is referred to as dispersion. A spectrum is a collection of colours. The separation of different colours of light by refraction is the dispersive power of a transparent medium.
Complete answer:
Initially, the dispersion was examined through a glass prism. It occurs because the refractive index of the medium's substance varies depending on the colour. The term "colours' ' refers to the wavelengths. The ratio of the difference in refractive index of two different wavelengths to the refractive index at some defined intermediate wavelength determines the dispersive power of any transparent medium.
Consider a glass prism as an example; a prism's refractive index is provided by the relationship
$\mu = \dfrac{{\sin \dfrac{{A + D}}{2}}}{{\sin \dfrac{A}{2}}}$
Where $A$ is the prism angle and $D$ is the minimum deviation angle. If $A$ is a small angled prism's refractive angle and is the angle of deviation $\delta $.
The prism formula is as follows:
$\mu = \dfrac{{\sin \dfrac{{A + \delta }}{2}}}{{\sin \dfrac{A}{2}}}$
Because we're talking about small angled prisms,
$\sin \dfrac{{A + \delta }}{2} = \dfrac{{A + \delta }}{2}\,and\,\sin \dfrac{A}{2} = \dfrac{A}{2} \\
\Rightarrow \mu = \dfrac{{\dfrac{{A + \delta }}{2}}}{{\dfrac{A}{2}}} \\
\Rightarrow \mu A = A + \delta \\ $
Therefore, $\delta = \left( {\mu - 1} \right)A$
If $\delta v$ and $\delta r$ are the deviations of the violet and red rays, the corresponding wavelengths are given as $\mu v$ and $\mu r$ . So, the angular dispersion is given as
${\delta _v} - {\delta _r} = \left( {{\mu _v} - {\mu _r}} \right)A$
The angular dispersion is known as the difference in deviation between extreme colours.If $\delta y$ and $\mu y$are the deviation and refractive index of an intermediate wavelength yellow,
${\delta _y} = \left( {{\mu _y} - 1} \right)A$
On dividing both equation, we get
$\dfrac{{{\delta _v} - {\delta _r}}}{{{\delta _y}}} = \dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y}}}$
The expression $\dfrac{{{\delta _v} - {\delta _r}}}{{{\delta _y}}}$ is known as dispersive power of the material of the prism and is denoted by $\omega $.
$\therefore \omega = \dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y}}}$
The ratio of angular dispersion for any two wavelengths to the deviation of mean wavelength is the dispersive power of a prism's material.The SI unit of dispersive power is $watt$.
Note:Violet rays have a higher deviation and refractive index than red rays. As a result, violet rays travel at a slower speed through glass than red rays. Yellow rays' refractive index and deviation are used as mean values.
Complete answer:
Initially, the dispersion was examined through a glass prism. It occurs because the refractive index of the medium's substance varies depending on the colour. The term "colours' ' refers to the wavelengths. The ratio of the difference in refractive index of two different wavelengths to the refractive index at some defined intermediate wavelength determines the dispersive power of any transparent medium.
Consider a glass prism as an example; a prism's refractive index is provided by the relationship
$\mu = \dfrac{{\sin \dfrac{{A + D}}{2}}}{{\sin \dfrac{A}{2}}}$
Where $A$ is the prism angle and $D$ is the minimum deviation angle. If $A$ is a small angled prism's refractive angle and is the angle of deviation $\delta $.
The prism formula is as follows:
$\mu = \dfrac{{\sin \dfrac{{A + \delta }}{2}}}{{\sin \dfrac{A}{2}}}$
Because we're talking about small angled prisms,
$\sin \dfrac{{A + \delta }}{2} = \dfrac{{A + \delta }}{2}\,and\,\sin \dfrac{A}{2} = \dfrac{A}{2} \\
\Rightarrow \mu = \dfrac{{\dfrac{{A + \delta }}{2}}}{{\dfrac{A}{2}}} \\
\Rightarrow \mu A = A + \delta \\ $
Therefore, $\delta = \left( {\mu - 1} \right)A$
If $\delta v$ and $\delta r$ are the deviations of the violet and red rays, the corresponding wavelengths are given as $\mu v$ and $\mu r$ . So, the angular dispersion is given as
${\delta _v} - {\delta _r} = \left( {{\mu _v} - {\mu _r}} \right)A$
The angular dispersion is known as the difference in deviation between extreme colours.If $\delta y$ and $\mu y$are the deviation and refractive index of an intermediate wavelength yellow,
${\delta _y} = \left( {{\mu _y} - 1} \right)A$
On dividing both equation, we get
$\dfrac{{{\delta _v} - {\delta _r}}}{{{\delta _y}}} = \dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y}}}$
The expression $\dfrac{{{\delta _v} - {\delta _r}}}{{{\delta _y}}}$ is known as dispersive power of the material of the prism and is denoted by $\omega $.
$\therefore \omega = \dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y}}}$
The ratio of angular dispersion for any two wavelengths to the deviation of mean wavelength is the dispersive power of a prism's material.The SI unit of dispersive power is $watt$.
Note:Violet rays have a higher deviation and refractive index than red rays. As a result, violet rays travel at a slower speed through glass than red rays. Yellow rays' refractive index and deviation are used as mean values.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers