Question

The air film in a Newton’s ring apparatus is replaced by an oil film. The radii of the rings
(A) Remains the same
(B) Increases
(C) Decreases
(D) None of the above

Answer 1

Hint:The Newton’s Ring method is a very basic method to calculate the wavelength of a monochromatic light using the concept of interference. In short, there is a constructive and destructive interference between the reflected and refracted light in the glass placed below the convex lens.

Formula used:
Newton found the following relation between the radius of nth BRIGHT ring and the wavelength of the monochromatic light used:
\[{r_N} = \sqrt {\lambda R\left( {N - \dfrac{1}{2}} \right)} \]
Where,
$\lambda $ is the wavelength of light use
R is the radius of curvature of the convex lens
${r_N}$ is the radius of nth BRIGHT ring

Complete step by step answer:
This concept was first described by Robert Hooke in 1664 but was studied in detail by Newton hence the name. The optical setup consists of a convex lens (usually with a very large radius of curvature) placed on a flat glass. The glass and lens only touch at the center. The gap between the lens and glass gradually increases towards the end and is filled with any fluid (usually it is an air film).
When viewed under a microscope, concentric alternate circles of bright and dark light are observed. This happens due to superposition which eventually leads to constructive and destructive interference. The light which gets reflected from the glass superpose with the incident light and the pattern is formed. The relation between the nth ring radius and the wavelength is given as:
\[{r_N} = \sqrt {\lambda R\left( {N - \dfrac{1}{2}} \right)} \]
This formula is applicable for air/vacuum. For any other fluid film, there is a minor change in the formula pertaining to wavelength as the wavelength changes in other mediums as:
\[{\lambda _m} = \dfrac{\lambda }{\mu }\]
Where,
${\lambda _m}$ is the wavelength in medium
$\mu $ is the refractive index of the fluid w.r.t air/vacuum
Therefore,
\[r_N^1 = \sqrt {{\lambda _m}R\left( {N - \dfrac{1}{2}} \right)} \\
  r_N^1 = \sqrt {\dfrac{\lambda }{\mu }R\left( {N - \dfrac{1}{2}} \right)} \\ \]
The radius thus reduces by a factor of $\dfrac{1}{{\sqrt \mu }}$.
The correct answer is option C.

Note:The newton’s ring method can also be used to calculate the radius of curvature of an unknown convex lens if we know the wavelength of light used. If you have been attentive, you would have noticed that the formula used is for the radius of nth bright ring. For radius of nth dark ring, the formula is:
\[{r_N} = \sqrt {\lambda RN} \]