Lab11_VanLe

Van Thin Le Professor Xiang Song Phys-2426-51700 22 November 2023 LAB 11: WAVE INTERFERENCE Part A Theory Please study Interference concept to answer the following questions. 1. Discuss interference, constructive and destructive interference. List the phase and path difference equations for constructive and destructive conditions.  Interference occurs when two or more waves superpose, combining their amplitudes and resulting in a new wave pattern. This phenomenon can be categorized into constructive and destructive interference .  Constructive Interference: This occurs when waves combine in such a way that their crests align with each other, resulting in an amplified wave with a larger amplitude. o Phase difference of two wave for CI: ∆ ϕ = ϕ 2 − ϕ 1 = 2 m π o The path difference for Bright: ∆r = r 2 − r 1 = m λ  Destructive Interference: This occurs when waves combine in such a way that the crest of one wave aligns with the trough of another, leading to a reduced or canceled-out wave. o Condition for out of phase (Dark): ∆ ϕ = ϕ 2 − ϕ 1 =( 2 m + 1 ) π o The path difference for Dark: ∆r = r 2 − r 1 =( 2 m + 1 ) λ 2 2. Discuss the Double Slits (Young’s) interference. Give path difference equation for the angle condition of interference in Young’s interference. Define the meaning of each term in your equation. In Young's double-slit interference experiment, a coherent light source passes through two closely spaced slits, creating two coherent wavefronts that overlap and interfere with each other on a screen placed some distance away. This produces a pattern of light and dark fringes known as interference fringes. Path difference: ∆r = r 2 − r 1 = dsinθ Constructive interference (bright) at point P: ∆r = dsin θ bright = m λ Destructive interference (dark) at point P: ∆r = dsin θ dark =( 2 m + 1 ) λ 2

3. Double slits interference shown in graph: slits separation d = 1900 nm, distance between slits and screen D = 4436 nm, central bright y o = 0, first bright position on screen y 1 = 1555 nm. Determine angle θ and wavelength λ using the given information. tanθ = ∆ y D = 1555 4436 →θ = tan − 1 ( 1555 4436 ) = 19.3 o d y D = m λ → d y 1 D = 1 × λ → λ = d y 1 D = 1900 × 1555 4436 = 666 nm 4. Discuss the phase change condition due to reflection of light from a surface. Summarize equations of interference for thin film. When light reflects from a denser medium to a rarer one, it undergoes a phase change of π (or 2λ/2). In interference within thin films, like soap bubbles, Equations dictate constructive interference when: 2 n 1 t =( 2 m + 1 ) λ 2 Equations dictate destructive interference when: 2 n 1 t = m λ Where:  t - the film's thickness  n1 - the surrounding medium's refractive index,  m - an integer representing fringe order,  λ - the light's wavelength in the film.

Red 1700 20.84 676.1 2.25 674.6 Green 1261 15.77 516.4 1.70 509.7 Violet 1015 12.8 421.2 1.40 419.7 Question: • If you decrease the Slits Separation d, what do you observe? The intensity of the remaining fringes reduces while the brightness of the bright fringe amplifies. • If you decrease the distance between Slits and Screen D, what do you observe? The intensity of the bright fringe grows, and this increase extends to the fringes nearing the center. II. Complete Data Table with Wave Interference/Interference Simulation: Basic Operation for Interference Simulation: Check Light Source (below Amplitude). Keep the default value on Frequency (green), Amplitude (Max), and Separation distance d = 1500 nm. Place check mark on Screen and Intensity. Press the Green Button on both Lights. Drag Ruler

out of Toolbox to measure the distance, D, between Light and Screen. Move Ruler to Screen (or Intensity) and measure the center-to-center distance Δy as shown in Figure of Table 1). Test and understand all functional tools on screen. You must practice figuring out what is the best way to complete the measurement. Data Table 2: Measure Wavelength λ of Light Source Measure the distance, D, between Light and Screen and measure the center-to-center distance Δy by Ruler . Referring to Young’s Interference, calculate wavelength λ=dsinθ. Drag Stopwatch out of Toolbox to measure 10 waves time as t 10 and calculate average period time T = t 10 /10. Calculate wavelength by λ T =cT, where c = 2.998 x 10 8 m/s. Separation distance: d = 1500 nm. 1 nm = 10 −9 m, 1fs = 10 −15 s. Measured the distance, D , between Slits and Screen: D = 4460.8nm Attach a Screenshot of Green Data from the Simulation to Lab Report . Color Δy (nm) θ=tan -1 (Δy/D) λ=dsinθ (nm) T (fs) λ T =cT (nm) Green 1710.3 21 537 1.85 554.6 Blue 1585 19.6 502.2 1.69 506.7 Violet 1371.3 17.1 440.76 1.45 434.7 Question: • Calculate the percent difference between λ and λ T of Green Data: % difference = {  Difference in Values  / [Average Value]}•100%