# To Determine  the wavelength  of  unknown  light  by  laser  diffraction  method

## To Determine  the wavelength  of  unknown  light  by  laser  diffraction  method

To Determine  the wavelength  of  unknown  light  by  laser  diffraction  method

THEORY:  If a  parallel  beam  of  light  of  wavelength  λ  is  coming  out  from  diffraction  grating,  placed  vertically  on  the   optical  bench  ,then  the  diffracted rays  from  the  grating  will  form  at  the  focal  plane  ,a  number  of  primary  maxima  of  different  order  numbers(n)  on  both  sides  of  the  central  maxima  of  zero  order.  If  θ  be  the  angle  of  diffraction  of  nth  order  primary  maxima  then  sinθ=mnλ  where  m  is  the  number  of  rulings  per  cm  of  the  grating  surface.

Hence,                     $m=\frac{\sin\theta}{n\lambda}$               Or,    $\lambda=\frac{\sin\theta}{nm}$

If  the  value  of  m  is  known  ,the  wavelength  λ  of  unknown  light  can  be  found  out.

PROCEDURE

Measuring the wavelength of the laser

1. Set up the laser and grating as shown in the figure.
2. Measure the distance L between the meter stick and the diffraction grating.
3. Turn on the laser and center the meter stick at the 0th order image.
4. Measure the distance s1 between the 1st order images appearing on the left and right sides of the center line.
5. Measure the distance s2 between the 2nd order images appearing on the left and right sides of the center line.

It should be clear from simple trigonometric considerations that

$\theta_{1}=arc\tan\frac{s_{1}}{2L}$
$\theta_{2}=arc\tan\frac{s_{2}}{2L}$

from which you can extract two independent measurements of the laser wavelength.

Experimental Results:

1 . Vernier constant for the horizontal scale of the microscope:

2.Table for the determination of the wavelength:

 Serial No. Order No. Orientation  from central maxima Reading for  Position of the detector θ Mean    θ Sin θ λ in cm Mean λ In nm M.S.R V.S.R Total 1 0 ——– ————————————— 2 1 Left Right 3 2 Left Right

Percentage Error:

$\frac{\partial \lambda}{\lambda}=\frac{\partial \sin\theta}{\sin\theta}+\frac{\partial m}{m}+\frac{\partial n}{n}$

( $$dm$$ =0,  $$dn$$ =0 )                                  $\frac{\partial \lambda}{\lambda}=\cot\theta d\theta$

Where  dθ=vernier constant of the laser spectrometer(in radian)

Hence, percentage  error=$\frac{\partial \lambda}{\lambda}\times100$

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