A diffraction grating having 550 lines/mm diffracts visible light at 33.0°. Part A What is the light's wavelength? Express your answer with the appropriate units. Α A= 990 nm 0 ? Submit Previous Answers Request Answer × Incorrect; Try Again; 4 attempts remaining

The Very Large Array (VLA) is a set of 27 radio telescope dishes in Catron and Socorro counties, New Mexico (Fig. P37.37). The antennas can be moved apart on railroad tracks, and their combined signals give the resolving power of a synthetic aperture 36.0 km in diameter. (a) If the detectors are tuned to a frequency of 1.40 GHz, what is the angular resolution of the VLA? (b) Clouds of interstellar hydrogen radiate at the frequency used in part (a). What must be the separation distance of two clouds at the center of the galaxy, 26 000 light-years away, if they are to be resolved? (c) What If? As the telescope looks up, a circling hawk looks down. Assume the hawk is most sensitive to green light having a wavelength of 500 nm and has a pupil of diameter 12.0 mm. Find the angular resolution of the hawks eye. (d) A mouse is on the ground 30.0 m below. By what distance must the mouses whiskers be separated if the hawk can resolve them? Figure P37.37

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?

In Figure P27.7 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4?

Blue light of wavelength 450 nm falls on a slit of width 0.25 mm. A converging lens of focal length 20 cm is placed behind the slit and focuses the diffraction pattern on a screen. (a) How far is the screen from the lens? (b) What is the distance between the first and the third minima of the diffraction pattern?

(a) A narrow beam of light containing yellow (580 nm) and green (550 nm} wavelengths goes from polystyrene to air, striking the surface at a 30.0° incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?

A hydrogen gas discharge lamp emits visible light at four wavelengths, =410 , 434, 486, and 656 nm. (a) If light from this lamp falls on a N slits separated by 0.025 mm, how far from the central maximum are the third maxima when viewed on a screen 2.0 m from the slits? (b) By what distance are the second and third maxima separated for l=486 nm?

(a) What visible wavelength has its fourth-order maximum at an angle of 25.0° when projected on a 25,000-line per centimeter diffraction grating? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

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.

An optical fiber has an index of refraction n and diameter d. It is surrounded by vacuum. Light is sent into the fiber along its axis as shown in Figure P34.31. (a) Find the smallest outside radius Rmin permitted for a bend in the fiber if no light is to escape. (b) What If? What result does part (a) predict as d approaches zero? Is this behavior reasonable? Explain. (c) As n increases? (d) As n approaches 1? (c) Evaluate Rmin assuming the fiber diameter is 100 m and its index of refraction is 1.40. Figure P34.31