Concept explainers
Suppose the slit width in Figure 37.4 is made half as wide. Does the central bright fringe (a) become wider, (b) remain the same, or (c) become narrower?
Figure 37.4 (a) Geometry for analyzing the Fraunhofer diffraction pattern of a single slit. (Drawing not to scale.) (b) Simulation of a single-slit Fraunhofer diffraction pattern.
Answer to Problem 38.1QQ
Explanation of Solution
Consider the figure given below.
Figure (1)
The condition for the central diffraction maximum is,
Here;
From the figure (1),
Here
From the trigonometry property, for very small angle,
Substitute
Substitute
For the case of central bright fringe, the order of the fringe is
Substitute
For
Rearrange the above equation for
Thus from above equation the central bright fringe width is inversely proportional to the slit width. Thus, if the slit width decreases or half of the initial value the width of central bight fringe increases.
Conclusion:
The width of the central bright fringe is inversely proportional to the slit width so, if the slit width decreases the width of central bright fringe increases. Thus option (a) is correct.
The slit width is half of the initial value and there is inverse dependence of width of central maxima and slit width so decrease in slit width widens the central bright fringe. Thus option (b) is incorrect.
The width of the central bright fringe is inversely proportional; so decrease in slit width will increase width. Thus option (c) is incorrect.
Want to see more full solutions like this?
Chapter 38 Solutions
PHYSICS:F/SCI.+.,V.2-STUD.S.M.+STD.GDE.
- Monochromatic light of wavelength l = 620 nm from a distant source passes through a slit 0.450 mm wide. The diffraction pattern is observed on a screen 3.00 m from the slit. In terms of the intensity I0 at the peak of the central maximum, what is the intensity of the light at the screen the following distances from the center of the central maximum: (a) 1.00 mm; (b) 3.00 mm; (c) 5.00 mm?arrow_forwardMonochromatic light of wavelength 622 nm is incident on a single-slit of width 0.321 mm. The diffraction pattern is observed on a screen 4.88 m from the slit. The intensity at the center of the central maximum is I_0. What is the distance (in mm) on the screen from the center of the central maximum to a point on the screen where the intensity has fallen to I_0/2?arrow_forwardIn the double-slit arrangement of Figure P36.13, d = 0.150 mm, L = 140 cm, = 643 nm. and y = 1.80 cm. (a) What is the path difference for the rays from the two slits arriving at P? (b) Express this path difference in terms of . (c) Does P correspond to a maximum, a minimum, or an intermediate condition? Give evidence for your answer. Figure P36.13arrow_forward
- Table P35.80 presents data gathered by students performing a double-slit experiment. The distance between the slits is 0.0700 mm, and the distance to the screen is 2.50 m. The intensity of the central maximum is 6.50 106 W/m2. What is the intensity at y = 0.500 cm? TABLE P35.80arrow_forwardA Fraunhofer diffraction pattern is produced on a screen located 1.00 m from a single slit. If a light source of wavelength 5.00 107 m is used and the distance from the center of the central bright fringe to the first dark fringe is 5.00 103 m, what is the slit width? (a) 0.010 0 mm (b) 0.100 mm (c) 0.200 mm (d) 1.00 mm (e) 0.005 00 mmarrow_forwardLight of wavelength 514 nm illuminates a slit of width 0.75 mm. At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.87 mm from the central maximum? 2.48 m 1.47 m 2.10 m 1.83 m nonearrow_forward
- In a double-slit interference experiment, a special lamp emitting yellow light from heated sodium atoms is used to produce an interference pattern on a screen located 1.39 m from a pair of slits separated by 0.12 mm. If the distance between adjacent bright regions in the resulting pattern is 6.83 mm, what is the wavelength (in nm) of the sodium light?arrow_forwardQUESTION 9 In a Young’s Double Slit Experiment light passes through two narrow slits of ? = 0.8 ??. The distance from double slit to the screen is 1.6 m. The distance from central fringe to the nth fringe is 5 cm. The wavelength of the light is 625 nm. The path difference correspond to A. a minimum B. a position between maximum and minimum. C. a maximum D. a maximum and minimumarrow_forwardTwo vertical slits of width 2.13 μm are separated by 24.4 μm and are illuminated by a laser with wavelength 514 nm. If a screen is placed at a distance of 1.96 m and we look at a location 23.8 cm horizontally from the center of the screen, what is the percentage of the single-slit intensity that we will see? [Include single-slit diffraction for this problem]arrow_forward
- Light of wavelength 520 nm illuminates a slit of width 0.45 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.52 mm from the central maximum? 0.45 m 0.53 m 0.63 m 0.72 m (b) Calculate the width of the central maximum. 1.04 mm 2.08 mm 3.12 mm 4.16 mmarrow_forwardA monochromatic light with 536nm pass through a slit that is 0.240 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum is 4.00 *10-5 W/m2. What is the intensity at a point on the screen the corresponding to θ=1.20˚?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning