Concept explainers
Consider a light wave passing through a slit and propagating toward a distant screen. Figure P37.53 shows the intensity variation for the pattern on the screen. Give a mathematical argument that more than 90% of the transmitted energy is in the central maximum of the diffraction pattern. Suggestion: You are not expected to calculate the precise percentage, but explain the steps of your reasoning. You may use the identification
Figure P37.53
Trending nowThis is a popular solution!
Chapter 38 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
- A quarter-wave plate is made from a material whose indices of refraction for light of free-space wavelength Ao = 589 nm are n = 1.732 and n = 1.456. What is the minimum necessary thickness of the plate for this wavelength?arrow_forwardDiffraction can be used to provide a quick test of the size of red blood cells. Blood is smeared onto a slide, and a laser shines through the slide. The size of the cells is very consistent, so the multiple diffraction patterns overlap and produce an overall pattern that is similar to what a single cell would produce. Ideally, the diameter of a red blood cell should be between 7.5 and 8.0 μm. If a 633 nm laser shines through a slide and produces a pattern on a screen 24.0 cm distant, what range of sizes of the central maximum should be expected? Values outside this range might indicate a health concern and warrant further study.arrow_forwardThe pupil of an eagle's eye has a diameter of 6.0 mm. Two field mice are separated by 0.010 m. From a distance of 166 m, the eagle sees them as one unresolved object and dives toward them at a speed of 24 m/s. Assume that the eagle's eye detects light that has a wavelength of 550 nm in vacuum. How much time passes until the eagle sees the mice as separate objects? t= i eTextbook and Mediaarrow_forward
- 10 mW of light is incident on a piece of GaAs which is 0.2mm thick. The incident light is a mixture of 5mW at λ1=1.553μm and 5mW at λ2=0.828μm. A total of 7mW mixed light exits out of the GaAs. Assume no reflections at the air/GaAs interface and any light generated by recombination won’t exit the GaAs. What are the absorption coefficients, α, for two different wavelengths?arrow_forwardFirst-order Bragg scattering from a certain crystal occurs at an angle of incidence of 63.8°; see figure below. The wavelength of the x-rays is 0.261nm. Assuming that the scattering is from the dashed planes shown, find the unit cell size ao. 63.8° X raysarrow_forwardIn the lab, you want to use a spectrometer to study the emission spectrum of a gas. This device works by having the light go through a diffraction grating and then carefully measuring the angle at which the light exits the grating. The problem is that the grating that you have is not labeled, so you do not know the spacing. To calibrate the spectrometer, you send a HeNe laser (wavelength 632.8nm) through the grating and observe it to exit at an angle of 37.6° in the second order by this grating. (For obscure technical reasons, the first order is not observable.) Light from the gas is then measured to be deflected by 34.9° in the second order. What is the wavelength of the light that is to be measured?arrow_forward
- An x-ray was used to examine a sample of chromium having a BCC crystal structure.Using x-rays having a wavelength of 0.1682 nm, a diffractometer is used. The distorting (010) aircraft is the plane. Chromium has an atomic radius of 0.125 nm. A)Compute the interplanar spacing and Calculate the diffraction angle. Assume second-order of diffraction, n = 2.arrow_forwardIn the figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.820 nm makes an angle θ = 62.3˚ with the top face of the crystal. What is the unit cell size a0?arrow_forwardThe following schematic shows the standing wave effect during the photolithography process. The UV light source has a wavelength of 360nm. If the refractive index (n) of the photoresist (PR) is 1.5. What is the thickness of the photoresist? PR tarrow_forward
- You measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (15.8 ± 0.2) cm, x2 = (6.7 ± 0.1) cm, and x3 = (11.3 ± 0.1). What is the uncertainty of the total distance x1 + x2 + x3? Group of answer choices 0.4 cm 0.5 cm 0.2 cm 0.3 cm 0.1 cmarrow_forwardAt the metal fabrication company where you work, you are asked to measure the diameter D of a very small circular hole in a thin, vertical metal plate. To do so, you pass coherent monochromatic light with wavelength 562 nm through the hole and observe the diffraction pattern on a screen that is a distance x from the hole. You measure the radius r of the first dark ring in the diffraction pattern. You make the measurements for four values of x. Your results are given in the table. (a) Use each set of measurements to calculate D. Because the measurements contain some error, calculate the average of the four values of D and take that to be your reported result. (b) For x = 1.00 m, what are the radii of the second and third dark rings in the diffraction pattern?arrow_forwardGallium arsenide (GaAs) is an expensive alloy used for high performance multijunction solar cells. A certain GaAs absorber layer is designed to absorb 95% of the incident red light = 700 nm. The complex refractive index of GaAs at this wavelength is given by ñGaAs = 3.77+ i0.141. By what fraction can the thickness of the GaAs absorber layer be decreased, if we introduce a lambertian scatterer at the front of the absorber layer and an ideal reflector at the back? Give a percentage [%]arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning