Air wedge (2)

AIR-WEDGE

Experiment-434

S

MEASUREMENT OF THICKNESS OF THIN OBJECTS USING THE AIR-WEDGE TECHNIQUE Jeethendra Kumar P K, Santhosh K and Sowmya* KamalJeeth Instrumentation & Service Unit, JRD Tata Nagar, Bengaluru-560092, INDIA *Student, Dept. of Electronics, Mangalore University, Mangalgangothri-574199

Email: [email protected] Abstract Using air-wedge microscope, polished glass plates, digital camera and Newton’s rings software the distance between two consecutive dark fringes is measured and the thickness of sample forming the air-wedge is calculated and compared with the thickness measured using a digital screw gauge.

Introduction There are several applications in physics where measurement of very thin objects like paper, mica, hair etc. is required. A screw gauge is generally used for this purpose. However, the measurement involves fixing the object in between the jaws of the screw gauge which exerts pressure on the object whose thickness is to be measured. This will, however, depend on how much pressure one exerts to hold the object between the jaws of the screw gauge. Therefore, for accurate measurement, one can use the air-wedge method, which is also suitable for measurement of thickness of a thin film deposited on a glass plate which may not be possible with a screw gauge. The air-wedge experiment for measurement of thickness of thin objects is an important experiment in physics labs.

The principle of air-wedge method When a piece of thin paper is introduced between two parallel transparent polished glass plates of 25mm x 75mm size, a wedge of air is trapped between the two glass plates. If the air wedge is now illuminated indirectly by a monochromatic light, using another turning glass plate positioned at 45° above the air wedge, as shown in Figure-1, the rays falling at an angle of 45° on the turning glass plate will get reflected down and fall on the upper glass plate of the air wedge. The ray of light travels from the rarer 1 KAMALJEETH INSTRUMENTS

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(air) to denser (glass) medium and again from glass (denser) to air (rarer) and finally reflected by the second glass plate. The rays get reflected and pass through the air wedge before finally getting reflected from the upper surface of the bottom glass plate of the air wedge. The light rays emerging again through the wedge and glass plates are collected by the objective of the travelling microscope and can be seen on the field of view of the microscope. Because of undergoing multiple reflections through the air wedge and glass plates, there will be phase difference between any two rays. These rays collected by the objective of the travelling microscope will interfere with one another and form interference fringes inside the tube of the microscope which can be viewed through the eye piece. Interference fringes thus produced contain alternate bright and dark fringes. To get such interference fringes the phase difference between the set of two rays is λ/2. Hence the path difference between the set of rays producing interference fringes with alternative light and dark fringes is λ/2.

Figure-1: The air wedge formed between two glass plates, illumination of the wedge by monochromatic light and collection of reflected rays by the objective of the telescope

Theory Figure-1 depicts the path of light ray and its capture by the travelling microscope. If A and B' are the positions of two consecutive dark fringes then the angle of inclination at the point of contact of two glass plates is related as ୆େ

Tanα = ୅େ

…1

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since AC=AB' This is the distance between two consecutive dark fringes, giving AB' = y To get bright and dark fringes the path difference between the rays must equal λ/2. This indicates the path difference as BC= λ/2 Substituting in Equation-1 λ

Tanα = ଶ୷

…2

Considering the larger triangle OPP' in Figure-1, we can also write ୔୔′ Tanα = ୓୔′

…3

PP' is the thickness of the paper (or any thin object) that forms the air wedge. Hence ୔୔′

௧

Tanα = ୓୔′ = ௟

…4

where OP'= l is the length of air wedge. Equating Equations- 2 and 4 we get Now equating Equation 2 and 4 we get λ ଶ୷

௧

=௟

Thus the thickness, t, of the object forming the air wedge is given by t=

ఒ௟ ଶ௬

…5

In this experiment by measuring the separation between two consecutive dark fringes (equal to the width of the bright fringe) the thickness of the object forming an air wedge is determined. The experiment provides a method of finding the thickness of very thin objects and thin films deposited on a glass plate. In case of thin objects like a sheet of paper , hair, thin metal wire, or a thin mica sheet, one can verify the thickness measured by employing the air wedge method with that obtained using a digital screw gauge to

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check the accuracy of the method for determining the thickness of thin films formed between two glass plates.

Measurement of fringe separation with a digital camera This experiment is part of our work on interfacing physics experiments with the PC or laptop. Hence in this experiment the naked-eye observation and measurement using micrometer are avoided. The same software used in the Newton’s rings is used here to observe and measure distance between two consecutive dark fringes.

Experimental set-up

Figure-2: The air-wedge formed between two glass plates and other samples The air-wedge glass plates and the thin samples, namely a sheet of paper, thin sheet of mica, and a copper strand used in this experiment are shown in Figure-2. Using a digital screw gauge the thickness of the sample is measured and tabulated in Table-1. The air-wedge experimental set-up used in the experiment is shown in Figure-3. It consists of a sodium vapour lamp set, air-wedge microscope and 45° turning glass plate. In addition to these, a digital vernier and digital screw gauge are also used for cross-checking the measurements made by the air wedge method. Table-1: Various samples and values of their thickness measured using digital screw gauge Sample Thickness (mm) Human hair 0.043 Paper 0.080 Mica 0.104 Copper 0.119 strand

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Figure-3: Air-wedge experimental set-up

Experimental procedure 1. The air-wedge microscope is illuminated with sodium vapour lamp set. The open- and closed ends of the air-wedge glass plates are identified.

Figure-4: Measurement of the distance ‘l’ using digital vernier 2. A reference line is drawn with a marker pen on the bottom glass plate about 5mm from the open end for placing the object for measuring its thickness. Using a digital vernier the distance between the closed end and the pen marking is noted as shown in Figure-4. The distance “l” between the closed end of the airwedge glass plate and the pen marking is given by

l= 6.5cm

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3. A piece of hair whose thickness is to be determined is now placed on the pen marking at the open end of the air-wedge glass plates and it is placed in the slot of the turning glass plate. 4. The air-wedge is now observed through the microscope and the 45° turning glass plate is adjusted such that straight line fringes are observed viewing through the eye piece, as shown in Figure-5.

Figure-5: Observed straight line fringes 5. Now the eye piece is removed from the travelling microscope and the digital camera is fitted in its place. The camera is connected to a lap-top or PC and following operations are performed. Open “My computer” Click on “USB Device”, the window “Take a new picture” Will appear on the screen

Figure-6: Display showing “Take a new picture” window

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Click on “take a new picture” which captures the image. Save and close this window. Next open the “Newton’s rings software”. The window as shown in Figure-7 will appear.

Figure-7: Newton’s rings software window

Fill the experimenter’s name and click on “load image” appearing at the bottom menu and select the captured image as explained. The captured image is shown in Figure-8.

Figure-8: Observed air wedge interference fringe pattern

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Click on “Set Origin” by pointing the mouse at the center of the image. Two crossed lines in green color will appear. Click on the leftmost fringe of the straight line fringe pattern. appear which is the ‘0’ th fringe.

A white line will

Now count 10 fringes to the right of the 0th fringe and point the cursor to the 10th fringe and click on it. Another white line will appear as shown in Figure-9 and Table on left of the window will show the distance between 0th and 10th fringe, which gives the width of 10 fringes. The distance between 10 fringes = 3898.05µm

Figure-9: White lines indicating distance between 10 fringes 6. Next click on column 2 in the table and the cursor is pointed on the 1st fringe to the right of the 0th fringe. A white line will appear. Moving the cursor to the 11 fringe and by clicking on it another white line will appear. Table on left of the window shows the distance between the 1 st and the 11th fringe. The total width of 10 fringes is noted for this case also. 7. This procedure is continued by selecting 10 fringes, 2-12, 3-13 etc. In each case the distance between 10 fringes is tabulated as shown in Figure-10.

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Figure-10: Selected fringes and their separation listed in table 8. The readings obtained are tabulated in Table-3. 9. Table-3: Fringe separation (= width of 10 fringes) Fringe numbers Width of 10 fringes (µm) 0-10 3898.05 1-11 3898.05 2-12 3845.84 3-13 3863.24 4-14 3950.65 5-15 3950.25 Average width of 3901.01 10 fringes From Table-3, the average width of 10 fringes = 3901.01µm. Hence, the fringe width y = 390.1µm The thickness or the diameter of the hair sample is calculated from Equation-5 as t=

λ௟ ଶ୷

=

ହ଼ଽ.ଷ୶ ଵ଴ షవ ୶଺ହ୶ଵ଴షయ ଶ୶ ଷଽ଴.ଵ୶ଵ଴షల

= 0.049mm

10. The experiment is repeated by replacing hair with a thin mica sheet, copper strand and a paper one by one. In each case the fringe width is measured and thickness is calculated as above. In the case of mica sheet or piece of paper, these

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are cut into a rectangular shape and while placing them, their left side should coincide with the mark made on the glass. Table-4: Thickness of various materials measured using the air-wedge method vis a vis the values measured by the screw gauge Material Fringe width Thickness of material (mm) (y)µm Air-wedge Screw gauge Hair 390.10 0.049 0.043 Mica 153.60 0.140 0.104 Copper 151.37 0.126 0.119 strand Paper 188.37 0.090 0.080

Results and discussion Table-4 shows thickness of the various materials measured using air-wedge method vis a vis the values measured with the digital screw gauge. For all the materials the thickness measured by the two methods is approximately same. Measurement of thickness of soft materials, such as paper, mica, hair, with a screw gauge will depend on the pressure applied to the screw gauge for holding the sample. Hence the thickness measured with the air-wedge method is more accurate as it does not depend on the subjective judgement of the experimenter as in the case of a digital screw gauge. This is evident from the measurement of thickness of a copper strand (which is a rigid body); whose diameter is found to be exactly same by both the methods.

Reference: [1]

S. P Basavaraju, A detailed text book of Engineering Physics Practicals, Page-27

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