S1 P So d S2 a b
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Figure shows an interferometer known as Fresnel’s biprism. The magnitude of the prism angle A is extremely small. (a) If S0 is a very narrow source slit, show that the separation of the two virtual coherent sources S1 and S2 is given by d = 2aA(n - 1), where n is the index of refraction of the material of the prism. (b) Calculate the spacing of the fringes of green light with wavelength 500 nm on a screen 2.00 m from the biprism. Take a = 0.200 m, A = 3.50 mrad, and n = 1.50.
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- Chapter 36, Problem 017 (a) Find the equation of a at which intensity extrema for single-slit diffraction occur (Im - is maximum). What are the (b) smallest a and (c) associated m, the (d) second smallest a and (e) associated m, and the (f) third smallest a and (g) associated m? (Note: To find values of a satisfying this conditiion, plot the curve y = tan a and the straight line y = a and then find their intersections, or use a calculator to find an appropriate value of a by trial and error. Next, from a = (m+1/2)x, determine the values of m associated with the maxima in the single-slit pattern. These m values are not integers because secondary maxima do not lle exactly halfway between minima.) (a) = 0 2 Edit •1 (b) a = Number Units 2 Units (c) m = Number *3 Units (d) a = Number *4 Units (e) m = Number Units (f) a = Number Units (g) m = NumberTwo slits are illuminated by a monochromatic plane wave of wavelength k. The slits have a width a=3k, and the distance between them is d=9k. (a) Determine if there are any interference maxima that are missing from the two-slit interference pattern because the minimum of the diffraction occurs in the same direction. Find all angles that lead to such missing orders. (b) Calculate the intensity of the first two-slit constructive interference fringe (|m|=1) relative to I(1), the intensity of the central peak.White light is incident on a diffraction grating with 2500 lines/cm. The screen is at a distance of 3.0 m. At what point nearest the central maximum will a maximum for red light (λ=600 nm) coincide with a maximum for violet light ( λ=400nm)? Identify the order of each maximum.
- Pls write clearlyLight with wavelength 633 nm is incident on a 2.50-μm-wide slit. Find the angular width of the central peak in the diffrac- tion pattern, taken as the angular separation between the first minima.Consider the following. (a) Find the angle ? locating the first minimum in the Fraunhofer diffraction pattern of a single slit of width 0.182 mm, using light of wavelength 581 nm.(b) Find the angle locating the second minimum.
- The analysis of any two-point source interference pattern and a successful determination of wavelength demands an ability to sort through the measured information and equating the values with the symbols in Young's equation. Apply your understanding by interpreting the following statements and identifying the values of y, d, m and L. Finally, perform some conversions of the given information such that all information share the same unit. If two slits 0.100 mm apart are separated from a screen by a distance of 300 mm, then the first-order minimum will be 1 cm from the central maximum. y= ________ d=________ m=_______ L=________To make a hologram using an Argon laser (1 = 0.488 µm), the maximum angle between objective and reference beams is 0max resolution (or spatial frequency) of the holographic recording film (fo – lines per mm)? 40°. What is the requirement on the minimum 0.633 um). Assume that z, When the hologram is reconstructed using a HeNe laser (A 10cm, z, = 2z,, Zp transversal and axial magnification (M; and Ma). = 00, please compute virtual and real image locations (Fz;), theConsider the following. (a) Find the angle (theta) locating the first minimum in the Fraunhofer diffraction pattern of a single slit of width 0.210 mm, using light of wavelength 555 nm.(b) Find the angle locating the second minimum.
- A monochromatic source of light of wavelength λ, is incident on a slit of width a. Obtain an expression to represent the angle of the 4th diffraction minimum. Hint: Think about Huygens construction with the single slit divided into four equal length sections acting as sources of secondary waves. Write down a general expression for the nth minimum angle. If λ =500 nm, a = 4 μm, determine the angle of the 2nd minimum.Monochromatic coherent light of amplitude E, and angular frequency w passes through three parallel slits, each sepa- rated by a distance d from its neighbor. (a) Show that the time-averaged intensity as a function of the angle 0 is I(0) = I (2nd sin e 1+ 2 cos max (b) Explain how this expression describes both the primary and the secondary maxima. (c) Determine the ratio of the intensities of the primary and secondary maxima. Hint: See Problem 16.The limit to the eye's acuity is actually related to diffraction by the pupil. What is the angle between two just-resolvable points of light for a 2.75 mm diameter pupil, assuming the average wavelength of 539 nm? angle between two points of light: Take the result to be the practical limit for the eye. What is the greatest possible distance a car can be from a person if he or she can resolve its two headlights, given they are 1.40 m apart? greatest distance at which headlights can be distinguished: m What is the distance between two just-resolvable points held at an arm's length (0.900 m) from a person's eye? distance between two points 0.900 m from a person's eye: m