In this video we will be performing one experiment which belongs to optics that is experiment of light and we are going to perform we are going to determine basically the wavelengths of the spectral line of the mercury source. with the help of transmission grating and by spectrometer. So we are going to use the principle of grating also at the same time we are going to use the apparatus which is known as spectrometer. So let us try to understand the concepts everything about spectrometer as well as the concept of grating and all other things for this experiment. So now let us see the apparatus used for this experiment.
First one is the source. This is the cabinet of the source. Inside this there is a source and here is a small slit for the light to come out. So this is source.
And what you see now is the spectrometer. This spectrometer is having three parts, basically three parts. First part, this part is basically collimator. Collimator is facing the source of light.
Now in this collimator there is a slit here and the slit width can be adjusted with the help of this screw. This screw is used to adjust the width of the slit. For focusing, this rack and pinion arrangement is there.
With the help of this rack and pinion, you can increase and decrease the distance between the slit and the lens. This is the lens and this is the slit. So this is the rack and pinion arrangement for adjustment of the distance between slit and the lens.
Next is these two screws. This screw is basically the lock. and this screw is for the adjustment of the horizontal level of the collimiter. So with the help of this we can change the horizontal level of the collimiter and when it is fixed, when it is exact, when I am sure that it is horizontal then I can lock with this with the help of this screw. This is about the collimiter.
The second part of the spectrometer is basically this bench. I will show you the bench separately. This is the bench.
In this bench, there are three screws. Screw number one, screw number two, and here is third screw, screw number three. With the help of these three screws, we can level this prism table.
The prism table can be made horizontal with the help of these three screws. Two screws are in one line and the third screw is at a point on the perpendicular bisector of the line joining these two screws. So obviously first we have to keep the spirit level along the line joining these two screws and when this is leveled then we are going to put it perpendicular in the perpendicular bisector and we are going to adjust it.
Then if in all both the direction the spirit level is centered then we can say this is horizontal. So this is the prism table. It is prism table but anything can be attached here which is going to be used for diffraction or interference or dispersion of light whatever be the instrument.
Then there is one screw you can see it here and this screw this screw is for loosening or varying the height of this prism table. With the help of this we can vary the height as per our requirement and when we tight it this becomes fixed. This prism table is basically fixed to this vernier scale.
It is attached with the vernier scale whereas the main scale is attached to this fixed disc. Main scale is fixed, the vernier scale can move with this prism table. And this is first one vernier.
This is the second vernier. You can choose anyone to be V1 and second to be V2. Suppose I choose this as V1, obviously this Vernier becomes V2.
So two verniers are there. Except this, there is third part of this instrument and this part is telescope. In the telescope, here is the field ends and here is the eyepiece.
Between these field ends and eyepiece, in between here there is a crossway. The distance of this... Eyepiece with respect to the lens can be changed again with the help of this rack and pinion.
With the help of this I can change the position of this eye lens with respect to the field lens. Now suppose I want to vary the distance between eyepiece and the crosshair then I can pull or push this eyepiece. See.
The eyepiece can be pulled out, it can be pushed in. By doing so, we can focus the cross wire on this eyepiece. So that is next thing about the spectrometer.
Now I am going to show you the scale of the spectrometer and you can see here, this is the scale of spectrometer. In this scale, you can see there is one scale which is fixed, the below scale which is fixed. And the second scale is movable scale. You can see it. It is moving.
So this is vernier. So vernier moves on the fixed scale. So it is a vernier but this vernier does not measure the length.
Instead it measures the angular separation. So this is the instrument for this is a vernier calipers for measuring the angular displacement. So this is vernier. And that's all about this instrument. Although there are few more screws are there, the function of that I have to tell you.
You can see this screw. This is the screw which locks the telescope. For locking the telescope I can use this screw.
When I tight it obviously this telescope gets locked. When telescope gets locked I cannot move it with my hand. And after locking this if I want small variation.
very feeble variation then with the help of this screw I can bring the feeble variations in the position of the telescope. That is all about this instrument. So first of all I am not showing you that I have made this level horizontal as well as this also horizontal because that you have done in your classes.
Now what we do? We keep the spectrometer in such a way that the slit is open to this slit of the source and the light enters the collimator and the light coming out of the collimator can be seen with the help of this naked eye. Now two observations are to be taken.
First one is for the adjustment of the spectrometer and second is for determination of the angular deviations. So, for adjusting the grating perpendicular to the incident beam, we have to do something. So, this is the incident beam.
Obviously, the axis of this collimator is going to be the path of the incident beam. So, this incident beam is going to come here like this. So, I must put the grating, transmission grating exactly perpendicular to this. And this is not to be done just by see I am adjusting it roughly no it should be exactly 90 degree. And for doing that we are using a principle that whenever the beam of incidence on a glass plate is going to be of 45 degree the reflected beam is going to get reflected by 45 degree.
So the angle between the incident beam and the reflected beam is going to be equal to exactly 90 degree. So first of all we try to keep this collimator and this telescope exactly at 90 degree. And when we are going to keep it 90 degree then we are going to keep the glass plate and we will try to reflect the beam which is coming from the collimator and entering the telescope. So first thing is to be...
adjusting the angle between this collimiter and telescope to be equal to 90 degree. For doing this What we do is, we try to bring the incident slit exactly at the cross wire of the telescope. So, we are bringing the incident slit exactly upon the cross wire of the telescope. And this is the position when the slit's image is being formed exactly at the cross wire of the telescope.
You can see now the slit, white slit is exactly on the vertical wire of the cross slit. So here you can see the reading. The upper scale is the vernier scale. And you can see the reference point that is 0 point of the vernier scale has crossed the 50th mark. Means the main scale reading is 50 degree.
And you can see the 10th division of the vernier is exactly coincident with any division of the main scale. So vernier scale division's value is 10. Main scale reading is 50.0 degree and the number of division on the vernier scale is 10. So now I add 90 degree to this because in this specific orientation these two are exactly in line. Now I want to keep them in 90 degree. So when they are exactly at line the reading is 50. in the main scale and 10 division in the vernier so when i add 90 to it the reading becomes 140 degree and 10th division of vernier so what i do i try to bring this in the reading of say 140 140 and the vernier scale division is going to be equal to 10 divisions So I am adjusting it.
I am moving the telescope towards one side and now I can show you the reading. It has exactly crossed 140 and the 10th division is coincident. Yes, now you can see the reading.
So you can see the vernier scale 0 has crossed 140. And this 10th division of vernier is coincident, 10th division is exactly coincident with any division of the main scale. So this is the grating frame on which the grating will be kept. And this frame is being fixed on this prism table.
There are two screws with the help of which I can fix it properly. So I fix the grating frame exactly at the center of the grating. Center of the prism table. So this is the position of the prism table.
Now grating stand has been fixed and this is grating. This is the grating. This is grating and in this grating so many things are written.
I will show you afterwards. The one grating is to be taken from this grating also. Now I fix this grating on the grating stand in this way.
There are the two clips. and with the help of clips I push it and I fix it on the prism table. Now the grating strength is on the grating is on the prism table.
Now what I have to do I have to rotate this complete prism table see when this is the collimator this is the ray coming and now I have kept approximately perpendicular to the perpendicular grating to the incident beam. Now I will rotate it slowly and I will try to find by rotating it in this way, I will try to find the reflected image of this ray at this telescope. Means the angle of incidence and angle of reflection will be exactly equal to 90. In that specific case, the angle of incidence on this grating will be of 45, exactly 45. So exactly opposite 45 degree rotation is going to keep migrating perpendicular to this incident B.
So let me do this, let me try this. I am going to try to find the position of the reflected image. Seeing from here, that is eyepiece, I am going to try to find, try to locate the reflected image exactly at the cross wire of this telescope. Yes, now you can see, I can show you in the telescope that the reflected beam has come exactly at the cross wire. You can see this is the reflected image of the slit.
at 90 degree. You can see it is exactly at the vertical cross wire. You can see here this is the collimator, this is the direction of the incident beam, it is the grating plane.
Grating plane is approximately 45 degree exactly sorry exactly 45 degree to the incident beam. That is why the reflected beam is again making an angle of 45 and that is why the angle between incident and reflected is exactly equal to 90 degree. Now we are sure that this grating is now making an angle of 45 degree with the incident beam.
So if I rotate it in opposite direction and by 45 degree, exact 45 degree, I am going to get the position of the grating exactly perpendicular to the collimiter or the incident beam. Now you can see the reading. When we have rotated and obtained the reflected image of the slit on the telescope when the telescope and collimator are at 90 degree, then the reading here you can see that the Vernier scale 0 has crossed the mark of 183.5.
It has crossed the mark of 183.5 and the Vernier scale reading that is the 7th division, you can see the 7th division. 7th division of the vernier is exactly coincident on any division of the main scale. Now as it is exactly inclined at 45 degree, I have taken the reading and the main scale reading was 183.5 and the vernier scale division was 7th.
So I have subtracted 45 degree from that to revert the prism table. to its position where the grating will be exactly at 90 degree to the incident. So the value becomes 183.5 minus 45 which is 138. So 138.5 should be the main scale reading and 7th division should be the vernier scale division.
So I am rotating it and I am bringing it to the position of 138.5. I want it at 138.5. So I am rotating back.
the prism table I am not touching the telescope you can you can see here this is 140 139 and this is 138.5 and 7th division 8th division coincident so this is the position where this collimator and this grating are exactly at 90 degree. You can see the position when the grating is exactly perpendicular to the incident. I have brought it to 138.5 main scale reading and the 8th division coincident.
You can see it, 8th division coincident. Now the adjustment is over. We have kept this grating perpendicular to the incident. Now we can start our experiment. Actually when the light gets incident on this transmission grating, the spectrums are formed.
The spectrum is going to be formed first order, second order, third order in one side of the transmission grating. At the second end also there will be first order, second order and third order grating. So to observe the grating orders, different spectrums, we bring back this telescope.
in line with the collimiter. When we bring it in this position, when we see through this eyepiece, we can see the white color slit, which is not the spectrum. I can get spectrum when I move either towards the left-hand side or towards the right-hand side.
In the left-hand side, when I am moving, I am going to get first-order spectrum, then second-order spectrum. then third order spectrum and so on. Similarly when I will be moving towards right hand side at certain position I am going to get the first order then second order then third order. So we will be focusing on first order only.
So let me show you how when we move from this position towards left hand side we are going to get spectrum and different colors of the spectrum. So, for getting the first order spectrum in the left hand side, I am moving this telescope towards the left hand side. of the central maxima which is colorless. As I go on moving at a certain angular distance I find this indigo color of the spectrum. First order spectrum indigo color.
You can see this is the indigo color. exactly on the vertical line of the cross layer. Now we are going to take the reading for this specific spectrum, first order spectrum in the left hand side. You can see the position of in the left hand side the indigo color if you see the zero of the vernier it is exactly at 23 degree.
It has crossed 23 and if you see the number of division which is matching is the fourth division which is exactly coincident with any division of the main scale. So main scale reading is 23.0 degree and the Vernier scale division's value is fourth division. We take the reading of the second Vernier also for this specific reading.
This is the reading of the first Vernier. See the reading here. The 0 has crossed 203 degree and if you see the division matching then this 29th division is exactly coincident with any division of the main scale. So the main scale reading for the second vernier is 203 degree, 203.0 degree and the vernier scale division is 29. Now after taking the reading of the indigo color, I move the telescope in the same direction, means towards left hand side, and I try to find the second color of the spectrum. And when I move it, I come to the second color, that is the green color which is visible here.
Can you see this? The green color is exactly on the vertical cross wire. Although it is adjacent for showing you the green color, but we have to keep the green color exactly, the cross wire exactly above the green color. And then we have to take the reading of this color.
Same, in the same way, if I go on moving in the same direction, I am going to get this yellow 1 and yellow 2 color. So, if you want to get the reading of yellow, you have to keep the cross wire. exactly in between these two yellow 1 and yellow 2. Here you can take the reading for yellow. Even if you move further you can get other color but those colors are as you can see blurred a little bit.
So we do not take the reading of that. So we are going to take the reading of this yellow color then this green color and as we have taken the indigo color. So these three colors reading we have to take in the left hand side.
So we have taken the reading of the spectrum towards left hand side first order only. In the same way we bring this again in its mean position then we move towards the right hand side. Again moving in the right hand side we will try to find the same colors same corresponding colors and here we reach in the right hand side the indigo color.
You can see this is the indigo color. We are going to take the first vernier reading, second vernier reading for this indigo. Again we are going to move further in the same direction.
You can see I am moving in the same direction and I reach the position where I get this green color. I bring the green color exactly on the cross wire and I take the reading of the green color. Again moving further I am going to get this yellow 1, yellow 2 as in that case. In this case also we are going to focus the cross wire in between yellow 1 and yellow 2 and we are going to take the reading of the yellow color.
Again if you move in the further direction you can see other colors are available but they are blurred, they are not focused, their position is not a definite angular position. That is why we do not take the reading of all other colors. We take the readings of this yellow which are focused green and as well as this.
indigo color. So these three colors reading we take. The next thing which we have to observe is we have to see the characteristics of the grating and in the characteristics the property which specifies the grating which is very important is written here. It is written 25,000 LPI means 25,000 lines drawn per inches.
So what is the meaning? The meaning is this. Suppose this distance is 2 inches. It is approximately 2 inches. Then in this, in the vertically 50,000 lines are there in 2 inches.
So obviously in 1 inch the number of lines drawn. By the diamond cutter is equal to 25000 lines. So in 1 inch the lines drawn are 25000. This is one more observation which we had to take that is the parameter of this grating and the parameter of the grating is how many lines per inches and it gives here the value is given here that is 25000 lines per inches. Next is the reading for adjusting the grating perpendicular to the incident beam.
So many other things we have taken, the number of lines per inches on the grating. As I have shown you, it is 25,000 lines per inches. So, depending on this, we can get the value of grating element, which is denoted as E, which is equal to 1 divided by N line N.
That is the lines per inches in inch. It is the grating element. 1 by n inches.
Or it is equal to if I convert inch into centimeter. Then it becomes equal to 2.54 divided by the number of lines per inches in centimeter. When I put the value 2.54 divided by 25000. It comes to be equal to 0.0001 centimeter.
So this is the value of the grating element. So first we have to determine the number of lines per inches on the grating. Then with the help of that you can determine the grating element either in inches or in centimeter. Because we are dealing here in centimeter that is why we have calculated in centimeter. Next is what is the Vernier constant because we are using Vernier scale.
So Vernier constant the smallest division of the main scale is 0.5 degree. divided by number of divisions on the vernier scale that is 60. So smallest division of the main scale divided by number of total number of divisions on the vernier scale gives us the vernier constant. If I put the value it is 0.5 divided by 60. 0.5 is value of one division of main scale. 60 is the total number of division on the vernier which is equal to 1 upon 120. And when calculated it becomes equal to 0.0083 degree. So this is the least count of the vernier used here for the measurement of angular separation.
Now we take the reading for adjustment. What we have done? First we have taken the reading of the telescope for direct image of slit in vernier 1. Here in this case we have taken one vernier only because it is adjustment. This is not.
actual reading taken. So, position of telescope on direct image of the slit, the value is main scale is division is 59, main scale value is 59 degree, vernier scale division is 10, this 10 multiplied by least count that is 0.0083 and added with 59 gives us 59.083 degree. So, when it is for direct image, if I want to keep the telescope perpendicular to the collimiter then with this reading i have to add 90 when added 90 it automatically became 149 main scale value and 10 divisions on the vernier scale which is equal to 149.083 degree so here we keep the telescope in this position we kept the telescope then we rotated the prism table To bring the reflected image of the slit on the cross wire, that was the position of 190 degree main scale reading, 19th division of the Vernier scale.
So total, this 19 multiplied by 0.0083, whatever comes added with 190 gives us the value of 190.158. So from this, this is the position when the grating is aligned. At 45 degree with respect to incident. So we subtract 45 from this.
And we get 145 degree and 19 division of the vernier. So this will be the position of the. the prism table and that will be fixed for the complete experiment because in this position the grating is exactly perpendicular to the incidence. As we have done the experiment for finding the value of deviation angular positions of the different color we have taken for indigo green and yellow for indigo Reading of the telescope of the spectrum on left hand side and right hand side. When we took the reading in the left hand side, we have taken the reading of first vernier and second vernier.
First vernier's position was 28.7 degree. Second vernier's position was 209.34 degree. For green, in the left side, the position of first vernier was 21.64 degree. Second vernier was 202.14 degree.
For yellow it was 19.58 degree and in second vernier's position was 199.84 degree. Similarly when we moved our telescope in the right hand side for indigo the two vernier's were having the reading of 81.32 and 261.18. For green the two vernier's were having reading of 88.58 and 268.37. And for yellow the reading was 90.84.
And 270.63. Now what we have to get is. The angular separation.
Between left and right position of the telescope. For the same color. That is for indigo.
The separation between. The first vernier in the left hand side. First vernier in the right hand side.
Is given here. Means C minus A. Or A minus C. Whichever is greater.
It is not actual difference. it is not actual subtraction but difference only. So, 81.32 minus 28 gives us the angular separation of 53.15. Similarly, the position of second vernier for the same color in right-hand side and left-hand side is 261.18 minus 209.34 which gives us the value of 51.84.
The average of these two is 52.50. So, this is the mean value of 2 theta. When divided by 2, it gives the value of angle that is theta. Similarly, for green color, we get the difference between 88.58 and 2164 written here and 268.37 minus 202. Here 66.94, 66.23, average is 66.59. Divided by 2 gives the position, angular position with respect to the central maxima to be equal to 33.29.
Similarly, for yellow, the value of 2 theta comes to be equal to 71.03 and the value of theta becomes 35.51. Now, we come to the part of calculation. The formula for what we wanted to determine is the wavelength lambda is equal to E sine theta divided by n, where E is the value of grating element, theta is the...
angular separation between central maxima and the maxima for that specific color and is the order of the spectrum. So we calculate for first for indigo color. For indigo we are putting the value of E which is equal to 0.001 multiplied by sin of the angle of deviation from the central maxima that is 26.25 degree divided by 1. which is the number of spectrum because we have taken the reading of first order spectrum only.
When calculated, it comes to be equal to 4.423 into 10 to the minus 5 centimeter or I can write it is 4.423 that is 4,423 into 10 to the minus 8 centimeter or 4,423 into 10 to the minus 10 meters or I can write it is 4,423 and strong. Similarly, when we calculate it for green, putting the value of theta for green, the value of the wavelength comes to be equal to 5489 angstrom. And when calculated for yellow, we get the value to be equal to 5808 angstrom, which is very near to the exact value of the wavelength of the different color. So we have done that. experiment as well as we have taken the reading and we have also calculated the value of different lambda of the different color that's all in this experiment