Newton’s Rings | Theory and Formula |

Newton’s rings

The thickness of the slowly increasing air film will form between the flat glass plate and the convex surface of the flat convex lens. The thickness of the air film will be zero at the point of contact and increases symmetrically as we move radially from the point of contact. The monochromatic wavelength light "λ" is allowed to fall normally on the lens with the help of a glass plate "P", which is held at 45 ° on the incident monochromatic beam. A portion of the incident light is reflected on the convex surface of the lens and the remaining light is transmitted through the air film. Then, a portion of this transmitted light is reflected from the upper surface of the glass plate (G).Both reflected rays combine to produce an interference pattern in the form of alternating flashes and a deep concentric ring known as Newton's rings. 

Arrangement of experiment of Newton’s rings

Newton first demonstrated and demonstrated these rings. The rings are spherical because the air film has spherical symmetry. These rings can be viewed through the mobile microscope . 

Newton’s rings as seen through microscope

Newton’s rings by reflected light theory

Let's discuss the interference conditions for bright and dark stripes and also the space between Newton's rings. To obtain the relationship between the radius of Newton's ring and the radius of curvature of the lens, consider the diagram Let the lens contact the glass plate at O and let the radius of curvature of the lens be R. Let go of a perpendicular ray. Partially reflected and partially transmitted in 'P'. The transmitted light is again reflected on the glass plate g in q. Let the thickness of the air film be PQ (= t) at P and the radius of the Newton ring at Q be rn. The reflected beam in Q undergoes a phase change different from the change or path λ / 2. The total path difference between two rays reflected in P 'and is Q' is

Calculation of film thickness from radius of curvature of lens

Th e lens is a part of sphere of radius ‘R’ with center‘C ’. From the property of circle

BA×AP= OA ×AD

 Newton’s rings formula

Newton's ring formula are shown in given figure below 

 Newton’s rings formula