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- An electric current through an unknown gas produces several distinct wavelengths of visible light. Consider the first order maxima for the wavelengths 403 nm, 428 nm, 511 nm, and 682 nm of this unknown spectrum, when projected with a diffraction grating of 5,000 lines per centimeter.Randomized Variablesλ1 = 403 nmλ2 = 428 nmλ3 = 511 nmλ4 = 682 nm Part (a) What would the angle (in degrees) be for the 403 nm line? Part (b) What would the angle (in degrees) be for the 428 nm line? Part (c) What would the angle (in degrees) be for the 511 nm line? Part (d) What would the angle (in degrees) be for the 682 nm line? Part (e) Using this grating, what would be the angle (in degrees) of the second-order maximum of the 403 nm line?arrow_forwardOne leg of a Michelson interferometer contains an evacuated cylinder of length L, =0.30m having glass plates on each end. A gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. If 140 bright fringes pass on the screen when light of wavelength A=440nm is used, what is n, the index of refraction of the gas? State your answer to the nearest 0.000001 ( one part per million).arrow_forwardFirst-order Bragg diffraction is observed at 23.8° relative to the crystal surface, with spacing between atoms of 0.24 nm. (a) At what angle will second order be observed? (b) What is the wavelength of the X-rays?arrow_forward
- A 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-orderdiffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?arrow_forwardThree discrete spectral lines occur at angles of 10.5°, 13.6°, and 14.7°, respectively, in the first-order spectrum of a diffraction grating spectrometer. (a) If the grating has 3770 slits/cm, what are the wavelengths of the light? ?1 = Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. nm (10.5°) ?2 = Your response differs from the correct answer by more than 10%. Double check your calculations. nm (13.6°) ?3 = Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. nm (14.7°) (b) At what angles are these lines found in the second-order spectra? ? = ° (?1) ? = ° (?2) ? = ° (?3)arrow_forwardThe width of the central peak in a single-slit diffraction pattern is 5.0 mm. The wavelength of the light is 600. nm, and the screen is 1.9 m from the slit. (a.) What is the width of the slit in microns? (D= ?) (b.) What is the ratio of the intensity at 4.2mm from the center of the pattern to the intensity at the center of the pattern? (I/I0= ?)arrow_forward
- In the single-slit diffraction experiment of the figure, let the wavelength of the light be 541 nm, the slit width be 6.11 pm, and the viewing screen be at distance D = 3.41 m. Let a y axis extend upward along the viewing screen, with its origin at the center of the diffraction pattern. Also let Ip represent the intensity of the diffracted light at point P at y = 15.8 cm. (a) What is the ratio of Ip the intensity Im at the center of the pattern? Determine where point P is in the diffraction pattern by giving the orders of nearest (b) maximum (0 is the central maximum) and (c) minimum between which it lies. Totally destructive interference- P1 12 Po Central axis a/2 Viewing screen Incident wave Units (a) Number 2.98e-4 This answer has no units Units (b) Number This answer has no units Version 4.24.1 2.arrow_forwardThe limit to the eye’s visual acuity is related to diffraction by the pupil.D = 2.85 mmdh = 1.25 m a. What is the angle between two just-resolvable points of light for a 2.85 mm diameter pupil in radians, assuming an average wavelength of 550 nm? θmin = b. Take your result to be the practical limit for the eye. What is the greatest possible distance in km a car can be from you if you can resolve its two headlights, given they are 1.25 m apart? L= c. What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye in mm? da =arrow_forwardCan you address a-b with the given information from the image?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_forwardLight of free-space wavelength 20 = 0.75 um is guided by a thin planar film of thickness d=2.5 μm and refractive index ni = 1.65, surrounded by a medium of refractive index n2 =1.45. (a) Determine (i) the critical angle Oc; (ii) the numerical aperture NA; and (iii) the maximum acceptance angle ao for light originating in air (no = 1.00). (b) Determine the number of TE modes possible at this wavelength. Determine (i) the propagation angle a and (ii) the propagation constant ß of the m= 0 TE mode (you will need to find a graphical or numerical approximate solution here). (iii) What is the wavelength of this mode inside the medium, measured along the z axis? (d) (i) Determine the extinction coefficient y for the same m= O mode. (ii) At what distance into the outer medium does the field drop to 1% of its magnitude at the boundary?arrow_forwardProblem 5: Consider light that has its third minimum at an angle of 24.4° when it falls on a single slit of width 3.55 µm . Randomized Variables e = 24.4 ° w = 3.55 µm Find the wavelength of the light in nanometers. 2 = 789 E AAL 4 |5 | 6 1| 2 sin() cos() tan() HOME cotan() asin() acos() atan() acotan() sinh() 3 cosh() tanh() cotanh() END O Degrees O Radians vol BACKSPACE DEL CLEAR Submit I give up! Hint Feedbackarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning