Osm Physics by Ashish

Michelson's Interferometer 1. Construction Michelson's interferometer is an optical instrument used to produce interference fringes by dividing a single beam of light into two coherent beams and then recombining them.   Its main components are: Monochromatic Light Source (S): Provides light of a single wavelength. Beam Splitter (G₁): A semi-silvered glass plate placed at 45° to the incident beam. It divides the incident light into two parts. Compensating Plate (G₂): A plane-parallel glass plate of the same material and thickness as the beam splitter. It ensures that both beams pass through equal thicknesses of glass. Mirrors M₁ and M₂: Plane mirrors placed perpendicular to each other. One mir...

Interference by transmitted rays Consider a plane-parallel transparent thin film of refractive index μ and thickness t . A ray of monochromatic light is incident on the upper surface of the film at an angle of incidence i . A part of the incident ray is reflected from the upper surface, while the remaining part is refracted into the film. let draw two perpendicular $C_2B$ and $P_2M$. then effective pathdifference $$\Delta_1 = \mu(C_1P_2 - P_2C_2)- C_1B \qquad ...(1)$$ $\because \Delta C_1MP_2 \approx \Delta C_2MP_2$ $$\therefore C_1P_2 = P_2C_2 = \frac{t}{\cos r} \qquad ...(2)$$ $$ and \qquad C_1M = MC_2 = t\tan r \qquad ...(3)$$ In $\Delta C_1AC_2$ $$\sin i = \frac{C_1A}{C_1C_2}= \frac{C_1A}{C_1N + NC_2}$$ Hence, $$C_1A = 2t \sin i \tan r \qquad..(4) \qquad \because eq.(3)$$ Thus by...

Interference in Reflected Rays Interference in Reflected Rays Consider a plane-parallel transparent thin film of refractive index μ and thickness t . A ray of monochromatic light is incident on the upper surface of the film at an angle of incidence i . A part of the incident ray is reflected from the upper surface, while the remaining part is refracted into the film. The refracted ray travels inside the film and make refraction angle r . It is partially reflected from the lower surface. The two reflected rays subsequently emerge in the same direction and interfere with each other. The interference between these two reflected rays depends upon the optical path difference between them. let draw two perpendicular $P_2A$ and $C_1M$. then effective pathdifference $$\Delta_1 = \mu(P_1C_1 - C_1P_2)- P_1A \qquad ...(1)$$ $\bec...

  Plane-parallel thin film A monochromatic light ray S S  is incident obliquely on the upper surface of the film at P 1 P_1 ​ with an angle of incidence i i . At P 1 P_1 , the incident ray is divided into a reflected ray R 1 R_1  and a refracted ray that enters the film at an angle r r . The refracted ray travels through the film and reaches the lower surface at C 1 C_1 , where it is again divided into a transmitted ray T 1 T_1 ​ and a reflected ray. This reflected ray travels upward to the upper surface at P 2 P_2 ​ , where a part emerges as the second reflected ray R 2 R_2 ​ , while the remaining part is reflected again towards the lower surface. In the same manner, repeated reflections and transmissions take place between the two parallel surfaces of the film, producing successive reflected rays R 1 , R 2 , R 3 , … R_1, R_2, R_3,\ldots  and transmitted rays T 1 , T 2 , … T_1,T_2,\ldots . Since all these emergent rays are parallel and originate from the same inci...

  The complete experimental arrangement for determining the wavelength of monochromatic light with the help of Fresnel’s biprism is shown in Figure. Suppose the light rays are deviated through an angle δ by the refracting faces of Fresnel’s biprism. If the angle of each prism is α and its refractive index is μ, then the angle of deviation is: δ = α(μ − 1) If the distance between the slit S and the biprism is a, then, according to Fig., d ⁄ 2 = a tan δ Since δ is very small, tan δ = δ Therefore, d ⁄ 2 = aδ Substituting the value of δ, d ⁄ 2 = aα(μ − 1) or, d = 2aα(μ − 1) If the distance between the biprism and the eyepiece is b, then the distance between the slit S and the eyepiece is: D = (a + b) If the width of the interference fringes is β, then: β = λD ⁄ d Therefore, λ = βd ⁄ D Substituting the values of d and D, λ = β[2aα(μ − 1)] ⁄ (a + b) Thus, the wavelength of monochromatic light can be determined using Fresnel’s biprism.

In this experiment, the thickness of a thin film is determined with the help of Fresnel’s biprism. Suppose the central bright fringe, which is initially formed at P 0 , is observed on the screen. Let the distance between the virtual coherent sources S 1 and S 2 be d , and the distance between the virtual sources and the screen be D . A transparent thin film of thickness t and refractive index μ is introduced in the path of one of the interfering beams. Due to the introduction of the film, the central bright fringe is displaced from P 0 to P 1 through a distance x. The optical path difference produced due to the thin film is: (μt − t) = t(μ − 1) The path difference corresponding to the displacement x of the fringe is: xd ⁄ D Therefore, ...

  Fresnel’s biprism is an optical device used to produce two coherent virtual sources from a single monochromatic source. It is used to demonstrate the interference of light and to determine the wavelength of monochromatic light . A Fresnel biprism consists of two thin prisms joined at their bases. It is equivalent to two thin prisms placed base-to-base. Structurally, the biprism acts as a single piece of optical glass with one obtuse angle (approx. 179°) and two small base angles (approx. 0.5°). When light from a narrow slit S  falls on the biprism: The upper half deviates the light in one direction. The lower half deviates the light in the opposite direction. The rays appear to come from two virtual images, S 1 ​ and S 2 ​ , of the original source S . Thus, S 1 ​ and S 2 ​ act as two coherent sources and produce interference fringes on the screen.

  There are two different methods of producing coherent sources: By division of the wavefront  Young's Double-Slit Experiment : A single source of monochromatic light illuminates a barrier with two closely spaced slits. The light emerging from these two slits acts as coherent sources. Fresnel's Biprism Method : A single wavefront is refracted through two adjacent, acute-angled prisms to produce two coherent virtual sources By division of the amplitude Newton's Rings: Light reflects back and forth between a spherical lens and a flat glass plate, dividing the amplitude to produce a coherent interference pattern.  Michelson's Interferometer: A beam splitter divides the amplitude of a light beam into two paths, which are then reflected by mirrors and recombined to create interference.