Concept explainers
(a)
To show: The point where
(a)
Answer to Problem 48AP
The point where
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The formula to calculate the intensity of the light is,
Here,
The value of
Substitute
Conclusion
Therefore, the point where
(b)
To draw: Plot
(b)
Answer to Problem 48AP
The graph between
Figure (1)
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The equation of
The solution of both the equation to coincide at a point is ,
So the solution of the transcendental equation is
(c)
To show: The angular full width at half maximum of the central diffraction maximum is
(c)
Answer to Problem 48AP
The angular full width at half maximum of the central diffraction maximum is
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The formula to calculate the phase angle is,
Rewrite the above equation for
If the value of
The path covered by the light is symmetric so the phase angle is double the initial value.
Substitute
Conclusion
Therefore, the angular full width at half maximum of the central diffraction maximum is
(d)
The number of steps involved to solve the transcendental equation
(d)
Answer to Problem 48AP
The number of steps involved to solve the transcendental equation
Explanation of Solution
Given info: The equation of the intensity of the light in the diffraction pattern is
The equation of
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The solution of the transcendental equation
Conclusion
Therefore, the number of steps involved to solve the transcendental equation
Want to see more full solutions like this?
Chapter 37 Solutions
Physics for Scientists and Engineers with Modern Physics
- Evaluate the formula xm= (L m 2) / D for single slit diffraction experiment.arrow_forwarda beam of white light is shined at normal incidence onto the outside of a soap bubble (index of soap solution = 1.340). An observer looking at the bubble, opposite to the direction of the beam, notices that green light (Lambda = 555.0 nm) is particularly bright in the reflected spectrum. What is the second thinnest wall thickness of the bubble?arrow_forwardQ/4 : In Biprism experiment the fringe width is 0.30 mm. If slits are covered by glass plate of thickness 0.04 mm and refractive index u = 1.5, then the fringe width is (a) 0.02 mm (b) 0.1 mm (c) 0.30 mm (d) 0.2 mmarrow_forward
- First-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_forwardProblem 1: In a double slit experiment the first minimum for 415 nm violet light is at an angle of 42°. Randomized Variables 2 = 415 nm e = 42 ° Find the distance between the two slits in micrometers. d= 8 9 5 6 sin() cos() tan() 7 HOME cotan() asin() acos() E A 4 atan() acotan() sinh() 1 2 3 cosh() tanh() cotanh() END O Degrees O Radians Vol BACKSPACE DEL CLEAR +arrow_forwardIn young's double slit experiment, the fringe width obtained by using monochromatic light of wavelength 6000 Å is 2 mm. If the whole apparatus is immersed in water of R. I. 1.33, then the change in fringe width will bearrow_forward
- Q. 36 : In young's double slit experiment, the obtained fringe width by using monochromatic light of wavelength 6000 A is 2 mm. If the whole apparatus is immersed in water of R. I. 1.33, then the change in fringe width will be (a) 1 mm (b) 1.2 mm (c) 1.5 mm (d) 0.5 mmarrow_forwardlet a beam of x rays of wavelength 0.125 nm be incident on an NaCl crystal at angle u 45.0° to the top face of the crystal and a family of reflecting planes. Let the reflecting planes have separation d = 0.252 nm. The crystal is turned through angle f around an axis perpendicular to the plane of the page until these reflecting planes give diffraction maxima. What are the (a) smaller and (b) larger value of f if the crystal is turned clockwise and the (c) smaller and (d) larger value of f if it is turned counterclockwise?arrow_forwardYour physics study partner tells you that the width of the central bright band in a single-slit diffraction pattern is inversely proportional to the width of the slit. This means that the width of the central maximum increases when the width of the slit decreases. The claim seems counterintuitive to you, so you make measurements to test it. You shine monochromatic laser light with wavelength λ onto a very narrow slit of width a and measure the width w of the central maximum in the diffraction pattern that is produced on a screen 1.50 m from the slit. (By “width,” you mean the distance on the screen between the two minima on either side of the central maximum.) Your measurements are given in the table. (a) If w is inversely proportional to a, then the product aw is constant, independent of a. For the data in the table, graph aw versus a. Explain why aw is not constant for smaller values of a. (b) Use your graph in part (a) to calculate the wavelength λ of the laser light. (c) What is…arrow_forward
- 632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 21.0°, what is the spacing between adjacent grooves in the grating? (In this problem, assume that the light is incident normally on the grating.) μm A helium-neon laser (1 =arrow_forwardA telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the Moon. If this is done with the Mount Wilson telescope, producing a 2.54 m diameter beam of 613 nm light, what is the minimum angular spread of the beam? Neglecting atmospheric effects, what is the size of the spot this beam would make on the Moon, assuming a lunar distance of 3.84×108 m?arrow_forwardA 475 nm wavelength spectral line is actually a doublet, 0.0043 nm separation. (a) What is the smallest number of lines that a diffraction network needs to have to separate this doublet in the 2nd order spectrum? (b) If this network is 10 cm long, in what direction will the line be observed in this spectrum? What will be the angular separation between the two components?arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax