grating-To study the diffraction phenomenon, wavelengths , difference between doublet wavelengths.

AIM: 1. To study the diffraction phenomenon,
          2. To determine the wavelengths of sodium yellow doublet.
          3. To find the difference between doublet wavelengths.

The phenomena of interference and diffraction are characteristic of a wave. The fact that light displays these phenomena brings out the wave nature of light under suitable experimental conditions. These phenomena as occurring for light have a wide range of applications. They can be used on the other hand to find the characteristics of light as a wave. Interference is simply addition or superposition of two sinusoidal waves. Diffraction is interference of waves around an obstacle placed in the path of a broad wavefront. Effects of diffraction become pronounced when the size of the obstacle is of the order of the wavelength of the wave. Such bending of waves around obstacles is called diffraction.

APPARATUS:  Spectrometer, plane transmission grating, grating stand,

                           monochromatic source of light, Spirit level, reading lens.

FORMULA: The condition for getting maximum intensity is,

(a + b) Sinq _n = nl

                 where, (a + b) is the grating element = [2.54/12386]cm,

                 l - wavelength of light used, (5893A⁰)

                 n - order of diffraction pattern,

                  q_n - angle of n^th order diffraction.

INTRODUCTION

The phenomena of interference and diffraction are characteristic of a wave. The fact that light displays these phenomena brings out the wave nature of light under suitable experimental conditions. These phenomena as occurring for light have a wide range of applications. They can be used on the other hand to find the characteristics of light as a wave. Interference is simply addition or superposition of two sinusoidal waves. Diffraction is interference of waves around an obstacle placed in the path of a broad wave front. Effects of diffraction become pronounced when the size of the obstacle is of the order of wavelength of the wave. Such bending of waves around obstacles is called diffraction.

THEORY

Assume a broad wave train – a plane monochromatic wave – falling normally on a transmission grating. The grating is an array of transparent and opaque, closely spaced, equidistant slit. The gratings are fabricated of a transparent solid material. The parallel rulings are carved on the surface with the help of a diamond scriber. The number of lines ruled is 6000 or more per centimeter.

We calculate path difference x between cylindrical waves (Huygens’ principle) emanating from adjacent transparent regions in a direction q (Fig.1)

x   =   (a + b) Sin q,

where, (a + b) is distance between centers of two adjacent transparent regions.

 If q is such that this path difference is an integral multiple of l (the wavelength), then the cylindrical waves from each transparent region interfere constructively in that direction and we get maximum intensity. Therefore, the condition for getting a maximum is,

                                       (a + b)Sinq_n = nl                                                (1)

Since, Sinq_n £ 1, for transmitted diffraction pattern n< (a + b)  ¤ l. We have labeled the q satisfying the condition for a particular n by q_n is called the angle of nth order diffraction. If q_n is known for any n,  l can be calculated. Thus, for a given grating, since (a + b) is fixed we can get only a finite number of diffraction orders.

For two wavelengths l₁ and l₂, which are very close to each other, if the angles of n^th order diffraction are taken as qn₁ and q_n2 then we get,

            Dl₁₂ = l₂ -l₁ = (a + b) (Sinq_n2 - Sinq_n1)/n    --------------(2)

PROCEDURE:

A. Adjustment of normal incidence

1. Rotate window so that line joining them makes an angle of approximately 45⁰ with collimator. Tighten screw to fix window position.

 2. Bring telescope in front of collimator to view slit directly. Adjust telescope crosswire on the slit. Read window W₁ (reading, say, x).

 3. Rotate telescope over window W₁ by 90⁰ changing W₁ reading to x ± 90⁰.Now the telescope axis is perpendicular to collimator axis. Fix telescope position by tightening screw.

  4. Set lines on grating table parallel to telescope axis. Mount the grating stand on the table exactly on one of the lines. Fix it with bolts.

 5. Rotate the top platform of the table (without rotating the windows) so that the reflected image of the slit is obtained on the cross wire in the telescope.

 6. Now release window and rotate windows by 45⁰. Grating face is now normal to light coming from collimator.

B.  Final leveling of grating table and adjustment of the slit 

     Free the telescope and rotate it so as to face the collimator and observe the slit directly through grating. Rotate it towards right slowly. You will first see the first order image of the slit then the second order image.

See whether the second order image is in the center of the view after you have focused it. If it is not adjusting , do the grating table leveling with screws to bring it the center.

Rotate the telescope now towards left passing through the direct image position so as to see first the order image and then the second order image.

See if the second order image is in the center of view. If it is not, again adjust the leveling screws on the prism table to bring it in the center.

Rotate the telescope back to RHS second order image and see that the image is still in the center. If not bring it to center by a further adjustment of leveling screws. Now focus the second order image properly in the telescope by adjusting the focusing. Decrease the slit width using DS1 so that the separation between the two lines you see is maximum and the intensity is enough to see the lines.

C. Recording the observations

1. Focus the telescope on d₂ line (outer) of the 2^nd order on RHS. Fix the telescope. Read both w₁ and w₂ readings. Record the readings.

2. Now bring cross wire on line d₁ by moving the fine movement screw. Read W1 and W2 and record readings. Release telescope.
3. Move the telescope so that the first order line d₁/d₂ comes in view. Fix the telescope. With fine movement screw align cross wire on d₁/d₂ line. Read W1,W2. Record  readings. Release telescope.
4. In similar manner record positions of the direct (zero^th order) line and first and second order lines on the LHS, always moving the telescope in the same direction.  

RESULTS
a. Wavelength of d1 line = l₁  A⁰ ----------
b. Wavelength of d2 line =l₂  A⁰ -----------
c. Separation of sodium doublet =Dl₁₂  A⁰ ----------

Answer following (any 5)

Q1. What is the smallest wavelength difference which you can reasonably measure with the equipment you have used?

Q2. Why slit width must be narrow?

Q3. You may observe the coloured lines along with the yellow one. Why is it so?

Q4. What is meant by coherent source?

Q5. What is grating? What modifications are required to extend the formula (a+b) sin θ_n = n λ for describing X ray diffraction?

Q6. Is the given source is point or broad source? What is the difference between them?

Q7. What will happen if number of lines is increased?

Q8. What value did you get for ∆λ? What is the actual value of ∆λ?

Q9. Calculate the least count of the spectrometer if there are 15 divisions covering 13 main scale divisions.

Q10. What is the function of collimator?

Q11. Why you observe two lines in second order and only a single line in first order?

Q12. What precautions do you take while noting down readings for first and second order on both sides?

Q13. How grating is constructed? Why the rulings are not visible?

Q14. State the principle of this experiment?

Q15. Why light is incident normally on the grating?