Purpose of the experiment:

  1.To observe Newton’s rings formed by the interface of produced by a thin air film;

2.To determine the radius of curvature of a plano-convex lens.

Basic Methodology:

When a plano-convex lens is put on a flat glass plate, a thin wedge shaped air film is created between the lower surface of the lens and upper surface of the glass plate. The thickness of the air film is very small at the point of contact and gradually increases from the center outwards. We fix these two glass together, it is called Newton’s rings equipment.

When a horizontal beam of light from a monochromatic source falls on the air film, a part of beam will reflected from the upper surface and the lower surface of the air film. When viewed with a microscope, interference takes place and bright and dark circular fringes are produced, the fringes are concentric circles.

Now let’s consider the light path difference Δ. If the thickness of the air film in this place is e, so we can get the value of Δ, which is not 2e, but 2e+0.5λ. Here an extra phase difference π occurs for the ray which got reflected from upper surface of the plate, this is because the incident beam in this reflection goes from a rarer medium to a denser medium. Thus the conditions for constructive and destructive interference (or bright rings and dark rings) are kλ and (2k+1)*0.5λ.

But, how can we get the value of R―the radius of curvature of the plano-convex lens? Look at this picture. Assuming that this r is radius of a certain dark ring, and e is the thickness of air film of corresponding dark ring. From the right-angle triangle we can get a equation:

Because the value of e is very smaller than R, so e² is neglected. So the equation become into this one: e=r²/2R. Putting the value of e into Δ, for dark rings, we can get r_k²=kRλ. Here r_k is the k^th order dark ring excluding the central dark spot.

To minimize the error, we can get d_m²=4mRλ and d_n²=4nRλ, so the equation for R is:

   (m=10,n=5)

Equipments:

Travelling microscope, Newton’s rings equipment, Sodium vapor lamp

Procedure:

1. Switch on the sodium vapor lamp and wait for a while until it send out monochromatic light;

2. Put the equipment on the stage and it center aims at object glass;

3. Adjust the half mirror to make scene bright enough;

4. Rotate the eyepiece to make cross wire clear and horizontal;

5. Adjust the focus wheel to move the object glass upwards to make Newton’s rings clear;

6. Let the cross wire aim at the center of Newton’s rings and divide into 4 same quarters;

6. Move the microscope to focus on the 10th order dark ring on one side of the center, set the cross wire tangential to it and write down the microscope reading;

8. Move the microscope to make the cross wire tangential to the 5th order dark ring in the same side, then the 5th, 10th order dark ring on the other side, write down these readings.

About reading:

The reading should include three parts of number: one comes from the vernier, the unit is millimeter; the other comes from the reading wheel, the unit is 0.01millimeter; and the third is estimate value.

Calculation: (λ=589.3nm)

Precautions:

1. Don’t move the object glass downwards when looking in eyepiece.

2. If you place the cross wire tangential to the outer side of a dark ring on one side of the central spot, then the cross wire should be placed to the inner side of the same ring on the other side of the central spot.

3. The travelling microscope should move only in one direction.