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21 White light shines through a grating onto a screen Describe the pattern that is produced 22 If blue light of wavelength 434 nm shines on a diffraction grating and the spacing of the resulting lines on a screen that is 105 m away is 055 m, what is the spacing between the slits in the grating 23 A diffraction grating with slits separated by 860 10 7 m is illuminated by violet light with a wavelength of 421 nm If the screen is 800 cm from the grating, what is the separation of the lines in the diffraction pattern 24 Blue light shines on the DVD in Example Problem 3 If the dots produced on a wall that is 065 m away are separated by 580 cm, what is the wavelength of the light 25 Light of wavelength 632 nm passes through a diffraction grating and creates a pattern on a screen that is 055 m away If the first bright band is 56 cm from the central bright band, how many slits per centimeter does the grating have



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Figure 19-15 The diffraction pattern of a circular aperture produces alternating dark and bright rings (Illustration not to scale)

One further expression for air-filled waveguide calculates the actual wavelength in the waveguide from a knowledge of the free-space wavelength and actual operating frequency:

In thin-film interference, the interference pattern is visible only within a narrow angle of view straight over the film This would be the case for the Morpho butterfly s blue, shimmering interference pattern, if not for the layer of glass-like scales on top of the layer of ground scales This glass-like scale layer acts as a diffraction grating and causes the blue, shimmering interference pattern to be spread to a diffraction pattern with a wider angle of view Scientists believe that this makes the Morpho butterfly more visible to potential mates

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The circular lens of a telescope, a microscope, and even your eye acts as a hole, called an aperture, through which light is allowed to pass An aperture diffracts the light, just as a single slit does Alternating bright and dark rings occur with a circular aperture, as shown in Figure 19-15 The equation for an aperture is similar to that for a single slit However, an aperture has a circular edge rather than the two edges of a slit, so slit width, w, is replaced by aperture diameter, D, and an extra geometric factor of 122 enters the equation, resulting in x1 122 L/D When light from a distant star is viewed through the aperture of a telescope, the image is spread out due to diffraction If two stars are close enough together, the images may be blurred together, as shown in Figure 19-16 In 1879, Lord Rayleigh, a British physicist, mathematician, and Nobel prize winner, established a criterion for determining whether there is one or two stars in such an image The Rayleigh criterion states that if the center of the bright spot of one star s image falls on the first dark ring of the second, the two images are at the limit of resolution That is, a viewer will be able to tell that there are two stars rather than only one If two images are at the limit of resolution, how far apart are the objects Using the Rayleigh criterion, the centers of the bright spots of the two images are a distance of x1 apart Figure 19-16 shows that similar triangles can be used to find that xobj/Lobj x1/L Combining this with x1 122 L/D to eliminate x1/L, and solving for the separation distance between objects, xobj, the following equation can be derived Rayleigh Criterion xobj.

D The separation distance between objects that are at the limit of resolution is equal to 122, times the wavelength of light, times the distance from the circular aperture to the objects, divided by the diameter of the circular aperture

Figure 19-16 Similar-triangle geometry allows you to calculate the actual separation distance of objects The blue and red colors are used only for the purpose of illustration (Illustration not to scale)

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where is the wavelength in the waveguide is the wavelength in free space o Fc is the waveguide cutoff frequency F is the operating frequency

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