Interference and Diffraction of Light (1) (1) (1) (1)

Name Sereen E. Idries Date Nov 20, 2023 Instructor Interference of Light Objective: The purpose of this experiment is to examine interference patterns formed by laser light passing through two slits and determine the wavelength. Theory When light passes through two slits, the two light rays emerging from the slits interfere with each other and produce interference fringes. The angle to the maxima (bright fringes) in the interference pattern is given by d sin sin = m , ( m = 0,1,2,3 ,… ) where d is the slit separation, θ is the angle from the center of the pattern to the m th maximum, λ is the wavelength of the light, and m is the inbterference order (0 for the central maximum, 1 for the first side maximum, 2 for the second side maximum, . . . counting from the center out). See Figure 2.1. Since the angles are usually small, the following approximation is used: sin sin = tan tan From trigonometry and Fig 2.1: tan tan = y m D where y m is the distance on the screen from the center of the pattern to the m th maximum and D is the distance from the slits to the screen as shown in Figure 2.1. The interference equation can thus be solved for the wavelength: ¿ d y m mD , ( m = 0,1,2,3, … )

Double Slit

I. Table 1 for Green Light Slits to screen distance (D) = 2462 nm Slit Separation (d) = 2250 nm Slit width (w) = 550 nm First Order (m = 1) Second Order (m = 2) Distance from center to side y m (nm) 834 1853 Calculated Wavelength (nm) 762.21 864.4 Average Wavelength: ¿ 813 nm Include below a screenshot with an interference pattern: Repeat the steps above but change the frequency to the middle of the blue range. II. Table 2 for Blue Light Slits to screen distance (D) = 2476 nm Slit Separation (d) = 1500 nm Slit width (w) = 200 nm First Order (m = 1) Second Order (m = 2) Distance from center to side (y m ) in nm 828 1826 Calculated Wavelength (nm) 502 553 Average Wavelength: ¿ 527 nm Include below a screenshot with an interference pattern:

III. For a fixed slit separation and width change the laser color from red to green and blue and record the distance y 1 between the first order (m = 1) and the central order of interference (m=0) . Slit Separation (d) = nm Slit width (w) = nm Wavelength (nm) y1(nm) red 1209 green 926 blue 788 How are the interference patterns changing (intensity and distance between the maxima ) assuming the same slit separation and slit width if you used a lasers with lower wavelength?