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Spectrometer: i-d curve
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Aim 

 

  • To determine the angle of prism (A).
  • Find the angles of deviation (d) corresponding to various angles of incidence and draw the i-d curve.
  • To determine the refractive index of the material of the prism.

 

Apparatus 

 

 Spectrometer, prism, prism clamp, sodium vapour lamp, lens. etc.

 

Principle 

 

When a beam of light strikes on the surface of transparent material(Glass, water, quartz crystal, etc.), the portion of the light is transmitted and other portion is reflected. The transmitted light ray has small deviation of the path from the incident angle. This is called refraction.

  

 Refraction is due to the change in speed of light while passing through the medium. It is given by Snell's Law.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨normal¨»sin«/mi»«mfenced»«mi»i«/mi»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»sin«/mi»«mfenced»«mi»r«/mi»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»n«/mi»«mn»2«/mn»«/msub»«msub»«mi»n«/mi»«mn»1«/mn»«/msub»«/mfrac»«/math»                -------------------(1)
 Willebrord Snel van Royen   (1580-1626)

Where«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»i«/mi»«/math» is the angle of incident and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math» is the angle of refraction. And «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»n«/mi»«mn»1«/mn»«/msub»«/math» is the refractive index of the first face and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»n«/mi»«mn»2«/mn»«/msub»«/math» is the refractive index of the second face.

 And the speed of light on both face is related to the equation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»c«/mi»«mn»1«/mn»«/msub»«msub»«mi»c«/mi»«mn»2«/mn»«/msub»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»n«/mi»«mn»2«/mn»«/msub»«msub»«mi»n«/mi»«mn»1«/mn»«/msub»«/mfrac»«/math»         -------------------(2)

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»c«/mi»«mn»1«/mn»«/msub»«/math» is the velocity of wave in first face and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»c«/mi»«mn»2«/mn»«/msub»«/math» is the velocity of wave in second face .

  

 

 Willebrord Snel van Royen           
(1580-1626)                        

   

 

Refractive index: It is the property of the matter, which determines how much light is bending, when light travelling through the it. 

 The refractive index of the material of the prism can be calculated by the equation.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»sin«/mi»«mfenced»«mfrac»«mrow»«mi»A«/mi»«mo»+«/mo»«mi»D«/mi»«/mrow»«mn»2«/mn»«/mfrac»«/mfenced»«/mrow»«mrow»«mi mathvariant=¨normal¨»sin«/mi»«mfenced»«mfrac»«mi»A«/mi»«mn»2«/mn»«/mfrac»«/mfenced»«/mrow»«/mfrac»«/math»              -------------------(3)

Where A is the angle of the prism and D is the angle of minimum deviation.

 

 

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