Light of wavelength 602 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin e= 0.23 and sin e = 0.34. The fourth-order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width, what are the (c) largest, (d) second largest, and (e) third largest values of the order number m of the maxima produced by the grating? (a) Number 5.5e-6 Units This answer has no units (b) Number 1.4e+0 Units This answer has no units (c) Number i 1 Units This answer has no units
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- A beam of monochromatic light is diffracted by a slit of width 0.605 mm. The diffraction pattern forms on a wall 1.38 m beyond the slit. The width of the central maximum is 1.75 mm. Calculate the wavelength of the light. 402.03 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 Need Help? Read ItMeasuring distance with high precision is a critical goal in engineering. Numerous devices exist to perform such measurements, with many involving laser light. Shining light through a double slit can be used to measure distance if (1) both the wavelength of the light beam and the distance between slits are known and (2) the spacing between the minima and maxima appearing on the screen can be measured. But this method requires a physical measurement of distance on the object, which may not be practical. To create a laser-based measurement device that does not require placing a physical ruler on the object, a Nd:YAG laser is mounted inside a box so that the beam of the laser passes through two slits rigidly attached to the laser. Although 1064 nm is the principal wavelength of a Nd:YAG laser, the laser can be switched to numerous secondary wavelengths, including 1052 nm, 1075 nm, 1113 nm, and 1319 nm. Laser Id Object The device is used to shine a beam on an object located nearby. The…Problem 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 +
- An instructor directs monochromatic light toward a single slit in an opaque barrier. The light has a wavelength of 550 nm and the slit is 0.230 mm wide. The light that passes through the slit creates a diffraction pattern on a screen, which is 1.65 m from the slit. (a) How wide (in mm) is the central maximum (the central, bright fringe), as measured on the screen? Single-slit diffraction is most readily described with a formula that gives the distance from the center of the pattern to the mth-order dark fringe. Consider the first dark fringe on either side of the central peak (m = ±1). How does its distance relate to the full width of the central maximum? Take care with units. mm (b) How wide (in mm) is either of the two first-order bright fringes, as measured on the screen? Single-slit diffraction is most readily described with a formula that gives the distance from the center of the pattern to the mth-order dark fringe. Consider two adjacent fringes on one side of the…Measuring distance with high precision is a critical goal in engineering. Numerous devices exist to perform such measurements, with many involving laser light. Shining light through a double slit can be used to measure distance if (1) both the wavelength of the light beam and the distance between slits are known and (2) the spacing between the minima and maxima appearing on the screen can be measured. But this method requires a physical measurement of distance on the object, which may not be practical. To create a laser-based measurement device that does not require placing a physical ruler on the object, a Nd:YAG laser is mounted inside a box so that the beam of the laser passes through two slits rigidly attached to the laser. Although 1064 nm is the principal wavelength of a Nd:YAG laser, the laser can be switched to numerous secondary wavelengths, including 1052 nm, 1075 nm, 1113 nm, and 1319 nm. Lo Id Object Laser The device is used to shine a beam on an object located nearby. The…Light of wavelength 616 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin 0 = 0.26 and sin 0 = 0.37. The fourth-order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width, what are the (c) largest, (d) second largest, and (e) third largest values of the order number m of the maxima produced by the grating?
- Light of wavelength 626 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin 0 = 0.26 and sin 0 = 0.34. The fourth-order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width, what are the (c) largest, (d) second largest, and (e) third largest values of the order number m of the maxima produced by the grating? (a) Number 6.26e-6 Units m (b) Number Units (c) Number Units (d) Number Units (e) Number UnitsThe full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See figure (b).) (a) Does the intensity drop to one-half the maximum value when sin²α = a²/2? (b) Is a = 1.39 rad (about 80°) a solution to the transcendental equation of (a)? (c) Is the FWHM AÐ = 2sin¹(0.442 A/a), where a is the slit width? Calculate the FWHM of the central maximum for slit width (d) 1.17 A, (e) 5.03 A, and (f) 11.7 A. 20 20 Relative intensity 15 10 0.8 0.6 a=2 0.4 0.2 5 05 8 (degrees) (a) 10 15 20 20 Relative intensity 1.0 0.8 0.6 -A0- 0.4 0.2 a= 52 20 15 10 5 0 5 10 15 20 (degrees) (b)(a) How many fringes appear between the first diffraction-envelope minima to either side of the central maximum in a double-slit pattern if λ = 691 nm, d = 0.120 mm, and a = 39.4 μm? (b) What is the ratio of the intensity of the third bright fringe to the intensity of the central fringe? (a) Number i 3 Units No units (b) Number 2.0E-4 Units No units