To determine the refractive index of a prism by using a spectrometer

: To determine the refractive index of a prism by using a spectrometer

Apparatus Required:
Spectrometer, prism, mercury vapour lamp, spirit level and reading lens. 

Formula Used: 

The refractive index μ of the prism is given by the following formula

Where A = angle of the prism, δm = angle of minimum deviation. 

Procedure: 

The following initial adjustments of the spectrometer are made first.  

• The spectrometer and the prism table are arranged in horizontal position by using the leveling screws.  

• The telescope is turned towards a distant object to receive a clear and sharp image. 

• The  slit is illuminated  by  a mercury  vapour lamp  and  the  slit  and  the  collimator  are  suitably adjusted to receive a narrow, vertical image of the slit.  

• The  telescope  is  turned  to  receive  the  direct  ray,  so  that  the  vertical  slit  coincides  with  the vertical crosswire. 

(A) Measurement of the angle of the prism:

• Determine the least count of the spectrometer. 

• Place the prism on the prism table with its refracting angle A towards the collimator and with its  refracting  edge  A  at  the  centre.  In  this  case  some  of  the  light  falling  on  each  face will  be reflected and can be received with the help of the telescope. 

• The telescope is moved to one side to receive the light reflected from the face AB and the cross wires are focused on the image of the slit. The readings of the two verniers are taken. 

• The telescope is moved in other side to receive the light reflected from the face AC and again the cross wires are focused on the image of the slit. The readings of the two verniers are taken. 

• The angle  through which  the  telescope is moved;  or  the  difference in  the  two  positions gives twice  of  the  refracting  angle  A  of  the  prism.  Therefore  half  of  this  angle  gives  the  refracting angle of the prism. 

(B) Measurement of the angle of minimum deviations: 

• Place the prism so that its centre coincides with the centre of the prism table and light falls on  one  of  the  polished  faces  and  emerges  out  of  the  other  polished  face,  after  refraction.  In  this  position the spectrum of light is obtained.  

• The  spectrum  is  seen  through  the  telescope  and  the  telescope  is  adjusted  for  minimum  deviation position for a particular colour (wavelength) in the following way: Set up telescope at  a particular colour and rotate the prism table in one direction, of course the telescope should be  moved in such a way to keep the spectral line in view. By doing so a positionwill come where a spectral line recede in opposite direction although the rotation of the table is continued in the same  direction.  The  particular position where the  spectral  line  begins  to  recede  in  opposite direction is the minimum deviation position for that colour. Note the readings of two verniers.

•Remove the prism table and bring the telescope in the line of the collimator. See the slit directly  through  telescope and  coincide  the image  of  slit with  vertical crosswire. Note  the  readings  of  the two verniers.  

• The difference in minimum deviation position and direct position gives  the angle of minimum  deviation for that colour.  

• The  same  procedure  is  repeated  to  obtain  the  angles  of  minimum  deviation  for  the  other  colours. 

Arrangement to determine the angle of prim

Arrangement to determine the angle of minimum deviation. 

Observations:    

1. Value of the one division of the main scale = ……… degrees            Total number of vernier divisions = ……….  Least count of the vernier = ………. degrees = ……… second
   

(ii) Table for the angle (A) of the prism.  

(iii) Table for the angle of minimum deviation (δm)

Calculations: 

Angle of the prism = ………  

Angle of minimum deviation for violet = ………..  

Refractive index for violet = …………..  

Angle of minimum deviation for blue = …………..  

Refractive index for yellow = ………….  

Angle of minimum deviation for red = ………..  

Refractive index for red = …………..  

Result: Refractive index for the material of the prism: 

Precautions and sources of error: 

(i) The telescope and collimator should be individually set for parallel rays.  

(ii) Slit should be as narrow as possible.  

(iii)While  taking  observations,  the  telescope and  prism  table  should  be  clamped with  the  help  of  clamping screws.  

(iv)Both verniers should be read.  

(v) The  prism  should  be  properly  placed  on  the  prism  table  for  the  measurement  of angle  of  the  prism as well as for the angle of minimum deviation.