Concept explainers
A horizontal laser beam of wavelength 632.8 nm has a circular cross section 2.00 nun in diameter. A rectangular aperture is to lie placed in the center of the beam so that when the light falls perpendicularly on a wall 4.50 m away, the central maximum fills a rectangle 110 mm wide and 6.00 mm high. The dimensions are measured between the minima bracketing the central maximum. Find the required (a) width and (b) height of the aperture. (c) Is the longer dimension of the central bright patch in the diffraction pattern horizontal or vertical? (d) Is the longer dimension of the aperture horizontal or vertical? (e) Explain the relationship between these two rectangles, using a diagram.
(a)
The width of the aperture.
Answer to Problem 38.4P
The width of the aperture is
Explanation of Solution
Given info: The wavelength of the laser beam is
Write the expression for the destructive interference.
Here,
Write the expression for the distance of the minimum from the central maximum.
Here,
The tangent is approximately equal to the sine if the angle is very small.
Substitute
Write the expression for the width of the central maximum.
Here,
Equate equation (1) and equation (2).
Substitute
Substitute
Conclusion:
Therefore, the width of the aperture is
(b)
The height of the aperture.
Answer to Problem 38.4P
The height of the aperture is
Explanation of Solution
Given info: The wavelength of the laser beam is
Write the expression for the height of the central maximum.
Here,
Substitute
Substitute
Conclusion:
Therefore, the height of the aperture is
(c)
Whether the longer dimension of the central bright patch is horizontal or vertical.
Answer to Problem 38.4P
The longer dimension of the central bright patch is horizontal.
Explanation of Solution
Given info: The wavelength of the laser beam is
From the given information, the width of the rectangle in the central bright patch is
Conclusion:
Therefore, the longer dimension of the central bright patch is horizontal.
(d)
Whether the longer dimension of the aperture is horizontal or vertical.
Answer to Problem 38.4P
The longer dimension of the aperture is vertical.
Explanation of Solution
Given info: The wavelength of the laser beam is
From part (a), the width of the aperture is
Conclusion:
Therefore, the longer dimension of the aperture is vertical
(e)
The relationship between the two rectangles.
Answer to Problem 38.4P
The longer dimension is
Explanation of Solution
Given info: The wavelength of the laser beam is
From part (a), the width of the aperture is
The smaller distance between aperture edges causes a wider diffraction angle.
Write the expression for the ratio of larger dimension to the smaller dimension of the aperture.
Substitute
Thus, the longer dimension is
Conclusion:
Therefore, the longer dimension is
Want to see more full solutions like this?
Chapter 38 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- A beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure P27.23. For what minimum nonzero value of the plate separation d is the transmitted light bright?arrow_forwardThe structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?arrow_forwardA glass tube with an internal diameter ofd = 50 cm and wall thickness of t = 5 cm is filled with chemical liquid. When a He-Ne laser light beam perpendicularly passes through this glass tube, the 1o). Assume that the coefficient of absorption 0.01 cm-1. Compute the coefficient of absorption of the liquid inside the tube. exit light energy (intensity) decreases by half (Ie of the glass is 2agarrow_forward
- (a) A small light fixture on the bottom of a swimming pool is 0.92 m below the surface. The light emerging from the still water forms a circle on the water surface. What is the diameter of this circle? (Give your answer, in m, to at least two decimal places.) Xm (b) What If? If a 1.63 cm thick layer of oil (noil = 1.35) is spread uniformly over the surface of the water, what is the diameter of the circle of light emerging from the swimming pool? (Give your answer, in m, to at least two decimal places.) X marrow_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. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) 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_forward. The velocity of light in the core of a step index fiber is 2.01 × 108 m s-1, and the critical angle at the core-cladding interface is 80°. Determine the numerical aperture and the acceptance angle for the fiber in air, assuming it has a core diameter suitable for consideration by ray analysis. The velocity of light in a vacuum is 2.998 x 103 m s-1arrow_forward
- A laser beam with wavelength λ = 550 nm hits a grating with n = 2250 grooves per centimeter. Part (b) Find the sin of the angle, θ2, at which the 2nd order maximum will be observed, in terms of d and λ. sin(θ2) =arrow_forwardA He-Ne gas laser which produces monochromatic light of a known wavelength ? =6.35 ? 10^7 ? is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?arrow_forwardWhen a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), wheret represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. dI Find the constant of proportionality k, where dt = kI. k = 0.462 What is the intensity of the beam 18 feet below the surface? (Give your answer in terms of I. Round any constants or coefficients to five decimal places.) 0' 0.00024arrow_forward
- Often in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0065 W to reach an intensity of I = 170 W/cm2 by focusing it through a lens of focal length f = 0.11 m. The beam has a radius of r = 0.0011m when it enters the lens. Randomized VariablesP = 0.0065 WI = 170 W/cm2f = 0.11 mr = 0.0011 Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?) Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.…arrow_forward(a) What is the intensity (in W/cm?) on the retina when looking directly at the sun? Assume that the eye's pupil has a radius rpupil = 1 mm. Take the Sun's irradiance at the earth's surface to be 1.1 kW/m?, and neglect refractive index (i.e. set n = 1). HINT: The Earth-Sun distance is do = 1.5 x 108 km and the pupil-retina distance is dį = 22 mm. The radius of the Sun rsun = 7.0 × 105 km is de-magnified on the retina according to the ratio d;/do.arrow_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_forward
- Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax