Aim: To observe Newton's rings and to determine the wavelength of monochromatic light (sodium light) using Newton's rings apparatus.
Apparatus Required
- A traveling microscope
- Sodium vapour lamp (monochromatic source)
- A plano-convex lens of large radius of curvature
- A flat optical glass plate
- A glass plate inclined at 45 degrees
- A magnifying glass
Theory & Principle
Newton's rings are an interference pattern caused by the reflection of light between two surfaces: a spherical surface and an adjacent flat surface. When a plano-convex lens is placed on a flat glass plate, a thin air film of varying thickness is formed between them.
When monochromatic light falls normally on this setup, light rays reflected from the top and bottom surfaces of the air film interfere with each other. This results in a pattern of concentric dark and bright rings around the point of contact.
Formula: The wavelength ($\lambda$) of the light used is given by:
$\lambda = \frac{D_{m+p}^2 - D_m^2}{4pR}$
Where:
$D_m$ = diameter of the $m^{th}$ dark ring
$D_{m+p}$ = diameter of the $(m+p)^{th}$ dark ring
$p$ = an integer representing the difference in ring numbers
$R$ = radius of curvature of the plano-convex lens
Procedure
- Clean the plano-convex lens and the flat glass plate. Place the lens on the plate such that its convex surface touches the plate.
- Arrange the 45-degree inclined glass plate above the lens-plate combination.
- Turn on the sodium vapour lamp and allow the light to fall horizontally on the inclined glass plate, which reflects it vertically downwards onto the air film.
- Focus the traveling microscope on the air film to view the interference pattern (concentric bright and dark rings with a dark central spot).
- Adjust the crosswire of the microscope so that its point of intersection lies on the center of the dark spot.
- Move the microscope carriage to one side (e.g., left) and align the vertical crosswire tangentially to the $20^{th}$ dark ring. Note the main scale and vernier scale readings.
- Move inwards and note the readings for the $16^{th}, 12^{th}, 8^{th}$, and $4^{th}$ dark rings.
- Cross the center and take readings for the corresponding rings on the other side (right side).
- Calculate the diameter ($D$) of each ring and then find $D^2$.
- Plot a graph of $D^2$ against the ring number ($n$). It should be a straight line. Use the slope of the graph to calculate the wavelength $\lambda$.
Observation Table
| Ring No. (n) | Microscope Reading (cm) | Diameter D = |Left - Right| (cm) | $D^2$ ($cm^2$) | |
|---|---|---|---|---|
| Left Side | Right Side | |||
| 20 | ||||
| 16 | ||||
| 12 | ||||
| 8 | ||||
| 4 | ||||
Result
The wavelength of the given monochromatic light (sodium light) is found to be _______ $\AA$ (Angstroms).
Precautions
- The glass surfaces must be perfectly clean. Dust particles can alter the air film thickness.
- The lens should have a large radius of curvature so the rings are well-separated and easy to measure.
- To avoid backlash error, the microscope screw should always be moved in one direction while taking readings on a particular side.
- The central spot must be perfectly dark. If it is bright, there is dust between the lens and the plate.
Viva Questions & Answers
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