Solved: What is the angular separation of the horizontal

Two sources emit waves that are coherent, in phase, and have wavelengths of 26.0 m. Do the waves interfere constructively or destructively at an observation point 78.0 m from one source and 143 m from the other source?

Repeat Problem 1 for observation points that are (a) 91.0 m and 221 m and (b) 44.0 m and 135 m from the two sources.

Two sources emit waves that are in phase with each other. What is the longest wavelength that will give constructive interference at an observation point 161 m from one source and 295 m from the other source?

Aperson driving at 17 m/s crosses the line connecting two radio transmitters at right angles, as shown in Figure 2831. The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at point A, the radio picks up a maximum net signal. (a) What is the longest possible wavelength of the radio waves? (b) How long after the car passes point A does the radio experience a minimum in the net signal? Assume that the wavelength has the value found in part (a).

Two students in a dorm room listen to a pure tone produced by two loudspeakers that are in phase. Students A and B in Figure 2832 hear a maximum sound. What is the lowest possible frequency of the loudspeakers?

If the loudspeakers in Problem 5 are 180 out of phase, determine whether a 185-Hz tone heard at location B is a maximum or a minimum.

Amicrophone is located on the line connecting two speakers that are 0.845 m apart and oscillating in phase. The microphone is 2.55 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphones location?

Amicrophone is located on the line connecting two speakers that are 0.845 m apart and oscillating 180out of phase. The microphone is 2.25 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphones location?

Moe, Larry, and Curly stand in a line with a spacing of 1.00 m. Larry is 3.00 m in front of a pair of stereo speakers 0.800 m apart, as shown in Figure 2833. The speakers produce a single-frequency tone, vibrating in phase with each other. What are the two lowest frequencies that allow Larry to hear a loud tone while Moe and Curly hear very little?

In Figure 2833 the two speakers emit sound that is 180 out of phase and of a single frequency, f. (a) Does Larry hear a sound intensity that is a maximum or a minimum? Does your answer depend on the frequency of the sound? Explain. (b)Find the lowest two frequencies that produce a maximum sound intensity at the positions of Moe and Curly.

Suppose the car radio in Problem 4 picks up a minimum net signal at point A. (a) What is the largest possible value for the wavelength of the radio waves? (b)If the radio transmitters use a wavelength that is half the value found in part (a), will the car radio pick up a net signal at point Athat is a maximum or a minimum? Explain. (c) What is the second largest wavelength that will result in a minimum signal at point A?

Consider a two-slit interference pattern, with monochromatic light of wavelength What is the path difference for (a) the fourth bright fringe and (b) the third dark fringe above the central bright fringe? Give your answers in terms of the wavelength of the light.

(a) Does the path-length difference increase or decrease as you move from one bright fringe of a two-slit experiment to the next bright fringe farther out? (b) What is in terms of the wavelength of the light

Predict/ExplainAtwo-slit experiment with red light produces a set of bright fringes. (a) Will the spacing between the fringes increase, decrease, or stay the same if the color of the light is changed to blue? (b) Choose the best explanation from among the following: I. The spacing between the fringes will increase because blue light has a greater frequency than red light. II. The fringe spacing decreases because blue light has a shorter wavelength than red light. III. Only the wave property of light is important in producing the fringes, not the color of the light. Therefore the spacing stays the same.

A two-slit experiment with blue light produces a set of bright fringes. Will the spacing between the fringes increase, decrease, or stay the same if (a) the separation of the slits is decreased, or (b) the experiment is immersed in water?

Laser light with a wavelength illuminates a pair of slits at normal incidence. What slit separation will produce rstorder maxima at angles of from the incident direction?

Monochromatic light passes through two slits separated by a distance of 0.0334 mm. If the angle to the third maximum above the central fringe is 3.21, what is the wavelength of the light?

In Youngs two-slit experiment, the rst dark fringe above the central bright fringe occurs at an angle of 0.31. What is the ratio of the slit separation, d, to the wavelength of the light, ?

A two-slit experiment with slits separated by produces a second-order maximum at an angle of 0.0990. (a) Find the wavelength of the light used in this experiment. (b) If the slit separation is increased but the secondorder maximum stays at the same angle, does the wavelength increase, decrease, or stay the same? Explain. (c) Calculate the wavelength for a slit separation of .

Atwo-slit pattern is viewed on a screen 1.00 m from the slits. If the two third-order minima are 22.0 cm apart, what is the width (in cm) of the central bright fringe?

Light from a HeNe laser strikes a pair of slits at normal incidence, forming a double-slit interference pattern on a screen located 1.40 m from the slits. Figure 2834 shows the interference pattern observed on the screen. What is the slit separation?

Light with a wavelength of 546 nm passes through two slits and forms an interference pattern on a screen 8.75 m away. If the linear distance on the screen from the central fringe to the rst bright fringe above it is 5.36 cm, what is the separation of the slits?

Aset of parallel slits for optical interference can be made by holding two razor blades together (carefully!) and scratching a pair of lines on a glass microscope slide that has been painted black. When monochromatic light strikes these slits at normal incidence, an interference pattern is formed on a distant screen. The thickness of each razor blade used to make the slits is 0.230mm, and the screen is 2.50 m from the slits. If the centerto-center separation of the fringes is 7.15 mm, what is the wavelength of the light?

Suppose the interference pattern shown in Figure 2834 is produced by monochromatic light passing through two slits, with a separation of , and onto a screen 1.20 m away. (a) What is the wavelength of the light? (b) If the frequency of this light is increased, will the bright spots of the pattern move closer together or farther apart? Explain.

Aphysics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least 2.50 cm. If the slits have a separation , what is the minimum distance from the slits to the screen when 632.8-nm light from a HeNe laser is used?

When green light passes through a pair of double slits, the interference pattern shown in Figure 2835(a) is observed. When light of a different color passes through the same pair of slits, the pattern shown in Figure 2835 (b) is observed. (a) Is the wavelength of the second color longer or shorter than 505 nm? Explain. (b) Find the wavelength of the second color. (Assume that the angles involved are small enough to set .)

The interference pattern shown in Figure 2835(a) is produced by green light with a wavelength of passing through two slits with a separation of . After passing through the slits, the light forms a pattern of bright and dark spots on a screen located 1.25 m from the slits. (a)What is the distance between the two vertical, dashed lines in Figure 2835 (a)? (b)If it is desired to produce a more tightly packed interference pattern, like the one shown in Figure 2835 (b), should the frequency of the light be increased or decreased? Explain.

Figure 2836 shows four different cases where light of wavelength reects from both the top and the bottom of a thin lm of thickness d. The indices of refraction of the lm and the media above and below it are indicated in the gure. For which of the cases will the two reected rays undergo constructive interference if (a) or (b) ?

The oil lm oating on water in the accompanying photo appears dark near the edges, where it is thinnest. Is the index of refraction of the oil greater than or less than that of the water? Explain.

Asoap bubble with walls 401 nm thick oats in air. If this bubble is illuminated perpendicularly with sunlight, what wavelength (and color) will be absent in the reected light? Assume that the index of refraction of the soap lm is 1.33. (Refer to Example 253 for the connection between wavelength and color.)

Asoap lm is 825 nm thick. White light strikes the lm at normal incidence. What visible wavelengths will be constructively reected if the lm is surrounded by air on both sides? (Refer to Example 253 for the range of visible wavelengths.)

White light is incident on a soap lm in air. The reected light looks bluish because the red light is absent in the reection. What is the minimum thickness of the soap lm?

A742-nm-thick soap lm rests on a glass plate . White light strikes the lm at normal incidence. What visible wavelengths will be constructively reected from the lm? (Refer to Example 253 for the range of visible wavelengths.)

An oil lm oats on a water puddle. You notice that green light is absent in the reection. What is the minimum thickness of the oil lm?

A radio broadcast antenna is 36.00 km from your house. Suppose an airplane is ying 2.230 km above the line connecting the broadcast antenna and your radio, and that waves reected from the airplane travel 88.00 wavelengths farther than waves that travel directly from the antenna to your house. (a) Do you observe constructive or destructive interference between the direct and reected waves? (Hint: Does a phase change occur when the waves are reected?) (b) The situation just described occurs when the plane is above a point on the ground that is two-thirds of the way from the antenna to your house. What is the wavelength of the radio waves?

Newtons Rings Monochromatic light with shines down on a plano-convex lens lying on a piece of plate glass, as shown in Figure 2837. When viewed from above, one sees a set of concentric dark and bright fringes, referred to as Newtons rings (See Figure 2811 for a photo of Newtons rings.). (a) If the radius of the twelfth dark ring from the center is measured to be 1.56 cm, what is the radius of curvature, R, of the lens? (b) If light with a longer wavelength is used with this system, will the radius of the twelfth dark ring be greater than or less than 1.56 cm? Explain.

Light is incident from above on two plates of glass, separated on both ends by small wires of diameter . Considering only interference between light reected from the bottom surface of the upper plate and light reected from the upper surface of the lower plate, state whether the following wavelengths give constructive or destructive interference: (a) ; (b) ; (c)

(a) What is the minimum soap-lm thickness in air that will produce constructive interference in reection for red light? (b) Which visible wavelengths will destructively interfere when reected from this lm? (Refer to Example 253 for the range of visible wavelengths.)

Athin layer of magnesium uoride is used to coat a int-glass lens . (a) What thickness should the magnesium uoride lm have if the reection of 565-nm light is to be suppressed? Assume that the light is incident at right angles to the lm. (b) If it is desired to suppress the reection of light with a higher frequency, should the coating of magnesium uoride be made thinner or thicker? Explain.

White light is incident normally on a thin soap lm suspended in air. (a) What are the two minimum thicknesses that will constructively reect yellow light? (b) What are the two minimum thicknesses that will destructively reect yellow light?

Athin coating is placed on a glass lens. Which visible wavelength(s) will be absent in the reected beam if (a)the glass has an index of refraction , and (b) the glass has an index of refraction ?

Two glass plates are separated by ne wires with diameters and , as indicated in Figure 2838. The wires are parallel and separated by a distance of 7.00 cm. If monochromatic light with is incident from above, what is the distance (in cm) between adjacent dark bands in the reected light? (Consider interference only between light reected from the bottom surface of the upper plate and light reected from the upper surface of the lower plate.)

A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if (a) the wavelength is doubled, (b) the slit width is doubled, or (c) the distance from the slit to the screen is doubled?

What width single slit will produce rst-order diffraction minima at angles of from the central maximum with 690-nm light?

Diffraction also occurs with sound waves. Consider 1300-Hz sound waves diffracted by a door that is 84 cm wide. What is the angle between the two rst-order diffraction minima?

Green light strikes a single slit at normal incidence. What width slit will produce a central maximum that is 2.50 cm wide on a screen 1.60 m from the slit?

Light with a wavelength of 676 nm passes through a slit wide and falls on a screen 1.85 m away. Find the linear distance on the screen from the central bright fringe to the rst bright fringe above it.

Repeat Problem 47, only this time nd the distance on the screen from the central bright fringe to the third dark fringe above it.

A single slit is illuminated with 610-nm light, and the resulting diffraction pattern is viewed on a screen 2.3 m away. (a) If the linear distance between the rst and second dark fringes of the pattern is 12 cm, what is the width of the slit? (b)If the slit is made wider, will the distance between the rst and second dark fringes increase or decrease? Explain.

How many dark fringes will be produced on either side of the central maximum if green light is incident on a slit that is wide?

The diffraction pattern shown in Figure 2839is produced by passing HeNe laser light through a single slit and viewing the pattern on a screen 1.50 m behind the slit. (a) What is the width of the slit? (b) If monochromatic yellow light with a wavelength of 591 nm is used with this slit instead, will the distance indicated in Figure 2839 be greater than or less than 15.2 cm? Explain.

A screen is placed 1.00 m behind a single slit. The central maximum in the resulting diffraction pattern on the screen is 1.60 cm widethat is, the two rst-order diffraction minima are separated by 1.60 cm. What is the distance between the two second-order minima?

Predict/Explain (a) In principle, do your eyes have greater resolution on a dark cloudy day or on a bright sunny day? (b) Choose the best explanation from among the following: I. Your eyes have greater resolution on a cloudy day because your pupils are open wider to allow more light to enter the eye. II. Your eyes have greater resolution on a sunny day because the bright light causes your pupil to narrow down to a smaller opening.

Is resolution greater with blue light or red light, all other factors being equal? Explain.

Two point sources of light are separated by 5.5 cm. As viewed through a -diameter pinhole, what is the maximum distance from which they can be resolved (a) if red light is used, or (b)if violet light is used

Aspy camera is said to be able to read the numbers on a cars license plate. If the numbers on the plate are 5.0 cm apart, and the spy satellite is at an altitude of 160 km, what must be the diameter of the cameras aperture? (Assume light with a wavelength of 550 nm.)

Splitting Binary Stars As seen from Earth, the red dwarfs Krger 60Aand Krger 60B form a binary star system with an angular separation of 2.5 arc seconds. What is the smallest diameter telescope that could theoretically resolve these stars using 550-nm light? (Note: )

Find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person (2.0 m) from an SR-71 Blackbird airplane ying at an altitude of 27 km. (Assume light with a wavelength of 450 nm.)

The Resolution of Hubble The Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.4 m in diameter. If the HST were to look down on Earths surface (rather than up at the stars), what is the minimum separation of two objects that could be resolved using 550-nm light? [Note: The HST is used only for astronomical work, but a (classied) number of similar telescopes are in orbit for spy purposes.]

Alens that is optically perfect is still limited by diffraction effects. Suppose a lens has a diameter of 120 mm and a focal length of 640 mm. (a) Find the angular width (that is, the angle from the bottom to the top) of the central maximum in the diffraction pattern formed by this lens when illuminated with 540-nm light. (b) What is the linear width (diameter) of the central maximum at the focal distance of the lens?

The resolution of a telescope is ultimately limited by the diameter of its objective lens or mirror. A typical amateur astronomers telescope may have a 6.0-in.-diameter mirror. (a) What is the minimum angular separation (in arc seconds) of two stars that can be resolved with a 6.0-in. scope? (Take to be at the center of the visible spectrum, about 550 nm, and see Problem 57 for the denition of an arc second.) (b) What is the minimum distance (in km) between two points on the Moons surface that can be resolved by a 6.0-in. scope? (Note: The average distance from Earth to the Moon is 384,400 km.)

Early cameras were little more than a box with a pinhole on the side opposite the lm. (a) What angular resolution would you expect from a pinhole with a 0.50-mm diameter? (b) What is the greatest distance from the camera at which two point objects 15 cm apart can be resolved? (Assume light with a wavelength of 520 nm.)

Agrating has 787 lines per centimeter. Find the angles of the rst three principal maxima above the central fringe when this grating is illuminated with 655-nm light.

Suppose you want to produce a diffraction pattern with X-rays whose wavelength is 0.030 nm. If you use a diffraction grating, what separation between lines is needed to generate a pattern with the rst maximum at an angle of 14? (For comparison, a typical atom is a few tenths of a nanometer in diameter.)

Adiffraction grating has 2200 lines/cm. What is the angle between the rst-order maxima for red light and blue light ?

Adiffraction grating with 345 lines/mm is 1.00 m in front of a screen. What is the wavelength of light whose rst-order maxima will be 16.4 cm from the central maximum on the screen?

The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it produces a rst-order principal maximum at an angle of 1.250. Calculate the number of lines per centimeter on the grating.

The second-order maximum produced by a diffraction grating with 560 lines per centimeter is at an angle of 3.1. (a)What is the wavelength of the light that illuminates the grating? (b) If a grating with a larger number of lines per centimeter is used with this light, is the angle of the second-order maximum greater than or less than 3.1? Explain.

White light strikes a grating with 7600 lines/cm at normal incidence. How many complete visible spectra will be formed on either side of the central maximum? (Refer to Example 253 for the range of visible wavelengths.)

White light strikes a diffraction grating (890 lines/mm) at normal incidence. What is the highest-order visible maximum that is formed? (Refer to Example 253 for the range of visible wavelengths.)

White light strikes a diffraction grating (760 lines/mm) at normal incidence. What is the longest wavelength that forms a second-order maximum?

Alight source emits two distinct wavelengths [ (violet); (orange)]. The light strikes a diffraction grating with 450 lines/mm at normal incidence. Identify the colors of the rst eight interference maxima on either side of the central maximum.

Alaser emits two wavelengths . When these two wavelengths strike a grating with 450 lines/mm, they produce maxima (in different orders) that coincide. (a) What is the order (m) of each of the two overlapping lines? (b) At what angle does this overlap occur?

When blue light with a wavelength of 465 nm illuminates a diffraction grating, it produces a rst-order principal maximum but no second-order maximum. (a)Explain the absence of higher-order principal maxima. (b)What is the maximum spacing between lines on this grating?

Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 2.10 m away. If the rstorder maxima are separated by 1.53 m on the screen, what is the distance between the two second-order maxima?

Adiffraction grating with a slit separation d is illuminated by a beam of monochromatic light of wavelength . The diffracted beam is observed at an angle relative to the incident direction. If the plane of the grating bisects the angle between the incident and diffracted beams, show that the mth maximum will be observed at an angle that satises the relation , with .

Monochromatic light with a wavelength passes through a single slit of width W and forms a diffraction pattern of alternating bright and dark fringes. (a) If the width of the slit is decreased, do the dark fringes move outward or inward? Explain. (b) What width is necessary for the rst dark fringe to move outward to innity? Give your answer in terms of .

Predict/Explain (a) If a thin liquid lm oating on water has an index of refraction less than that of water, will the lm appear bright or dark in reected light as its thickness goes to zero? (b)Choose the bestexplanationfrom among the following: I. The lm will appear bright because as the thickness of the lm goes to zero the phase difference for reected rays goes to zero. II. The lm will appear dark because there is a phase change at both interfaces, and this will cause destructive interference of the reected rays.

If the index of refraction of an eye could be magically reduced, would the eyes resolution increase or decrease? Explain

In order to increase the resolution of a camera, should its f-number be increased or decreased? Explain.

Diffraction effects often involve small angles, and we usually make the approximation . To see how accurate this approximation is, complete the following table.

When reading the printout from a laser printer, you are actually looking at an array of tiny dots. If the pupil of your eye is 4.3 mm in diameter when reading a page held 28 cm from your eye, what is the minimum separation of adjacent dots that can be resolved? (Assume light with a wavelength of 540 nm, and use 1.36 as the index of refraction for the interior of the eye.)

The headlights of a pickup truck are 1.32 m apart. What is the greatest distance at which these headlights can be resolved as separate points of light on a photograph taken with a camera whose aperture has a diameter of 12.5 mm? (Take .)

Antireection Coating A glass lens has an antireection coating of . (a) For 517-nm light, what minimum thickness of will cause the reected rays and in Figure 2840to interfere destructively, assuming normal incidence? (b) Interference will also occur between the forwardmoving rays and in Figure 2840. What minimum thickness of will cause these two rays to interfere constructively?

White light reected at normal incidence from a soap bubble in air produces an interference maximum at but no interference minima in the visible spectrum. (a) Explain the absence of interference minima in the visible. (b)What are the possible thicknesses of the soap lm? (Refer to Example 253 for the range of visible wavelengths.)

Athin lm of oil oats on water . When sunlight is incident at right angles to this lm, the only colors that are enhanced by reection are blue (458 nm) and red (687 nm). Estimate the thickness of the oil lm.

The yellow light of sodium, with wavelengths of 588.99 nm and 589.59 nm, is normally incident on a grating with 494 lines/cm. Find the linear distance between the rst-order maxima for these two wavelengths on a screen 2.55 m from the grating.

A thin soap lm suspended in air has a uniform thickness. When white light strikes the lm at normal incidence, violet light is constructively reected. (a) If we would like green light to be constructively reected, instead, should the lms thickness be increased or decreased? (b) Find the new thickness of the lm. (Assume the lm has the minimum thickness that can produce these reections.)

A thin lm of oil oats on water . When sunlight is incident at right angles to this lm, the only colors that are absent from the reected light are blue (458 nm) and red (687 nm). Estimate the thickness of the oil lm.

Sodium light, with a wavelength of , shines downward onto the system shown in Figure 2837. When viewed from above, you see a series of concentric circles known as Newtons rings. (a) Do you expect a bright or a dark spot at the center of the pattern? Explain. (b) If the radius of curvature of the plano-convex lens is , what is the radius of the tenth-largest dark ring? (Only rings of nonzero radius will be counted as rings.)

Figure 2839 shows a single-slit diffraction pattern formed by light passing through a slit of width and illuminating a screen 0.855 m behind the slit. (a)What is the wavelength of the light? (b)If the width of the slit is decreased, will the distance indicated in Figure 2839 be greater than or less than 15.2 cm? Explain.

Entoptic HalosImages produced by structures within the eye (like lens bers or cell fragments) are referred to as entoptic images. These images can sometimes take the form of halos around a bright light seen against a dark background. The halo in such a case is actually the bright outer rings of a circular diffraction pattern, like Figure 2821, with the central bright spot not visible because it overlaps the direct image of the light. Find the diameter of the eye structure that causes a circular diffraction pattern with the rst dark ring at an angle of 3.7 when viewed with monochromatic light of wavelength 630 nm. (Typical eye structures of this type have diameters on the order of . Also, the index of refraction of the vitreous humor is 1.336.)

White light is incident on a soap lm suspended in air. If the incident light makes a 45 angle with the normal to the lm, what visible wavelength(s) will be constructively reected? (Refer to Example 253 for the range of visible wavelengths.)

Asystem like that shown in Figure 2826 consists of N slits, each transmitting light of intensity . The light from each slit has the same phase and the same wavelength. The net intensity I observed at an angle due to all N slits is In this expression, , where is the wavelength of the light. (a) Show that the intensity in the limit is . This is the maximum intensity of the interference pattern.(b)Show that the rst points of zero intensity on either side of occur at and . (c) Does the central maximum of this pattern become narrower or broader as the number of slits is increased? Explain.

Two plates of glass are separated on both ends by small wires of diameter d. Derive an expression for the condition for constructive interference when light of wavelength is incident normally on the plates. Consider only interference between waves reected from the bottom of the top plate and the top of the bottom plate.

Acurved piece of glass with a radius of curvature Rrests on a at plate of glass. Light of wavelength is incident normally on this system. Considering only interference between waves reected from the curved (lower) surface of glass and the top surface of the plate, show that the radius of the nth dark ring is

The Resolution of the EyeThe resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter is 4.25 mm? Assume light with a wavelength of . (Note: The distance from the pupil to the retina is 25.4 mm. In addition, the space between the pupil and the retina is lled with a uid whose index of refraction is .

What is the minimum angle your eye can resolve, according to the Rayleigh criterion and the above assumptions? A. B. C. D

What is the linear separation between horizontal lines on the screen? A. 0.0235 mm B. 0.145 mm C. 0.369 mm D.

What is the angular separation of the horizontal lines as viewed from a distance of 12.0 feet? A. B. C. D

According to the Rayleigh criterion, what is the closest you can be to the TV screen before resolving the individual horizontal lines? (In practice you can be considerably closer than this distance before resolving the lines.) A. 3.51 ft B. 4.53 ft C. 11.5 ft D. 14.0 ft

Referring to Example 282 Suppose we change the slit separation to a value other than , with the result that the linear distance to the tenth bright fringe above the central bright fringe increases from 12 cm to 18 cm. The screen is still 2.3 m from the slits, and the wavelength of the light is 440 nm. (a) Did we increase or decrease the slit separation? Explain. (b) Find the new slit separation.

Referring to Example 282The wavelength of the light is changed to a value other than 440 nm, with the result that the linear distance to the seventh bright fringe above the central bright fringe is 12 cm. The screen is still 2.3 m from the slits, and the slit separation is . (a) Is the new wavelength longer or shorter than 440 nm? Explain. (b) Find the new wavelength.

Referring to Example 285The light used in this experiment has a wavelength of 511 nm. (a) If the width of the slit is decreased, will the angle to the rst dark fringe above the central bright fringe increase or decrease? Explain. (b) Find the angle to the rst dark fringe if the reduced slit width is .

Referring to Example 285 The width of the slit in this experiment is . (a) If the frequency of the light is decreased, will the angle to the rst dark fringe above the central bright fringe increase or decrease? Explain. (b) Find the angle to the rst dark fringe if the reduced frequency is