A line source of sodium light ( 0 = 589.3 nm) illuminates a Lloyds mirror 10.0 mm above its surface. A viewing screen is 5.00 m from the source and the whole apparatus is in air. How far apart are...

Show that α for the Fresnel biprism of Fig. 9.23 is given by α = 2d(n - 1)α. Fig. 9.23 Shield (a) Shield (b) Screen 20 R ry S, (c)

Two narrow slits in a thin metal sheet are 2.70 mm apart centerto-center. When illuminated directly by plane waves (in air) a fringe pattern appears on a screen 4.60 m away. It is found that...

Return to Fig. 2.25 and prove that if two electromagnetic plane waves making an angle θ have the same amplitude, E 0 , the resulting interference pattern on the yx-plane is a...

Show by direct calculation, using Mueller matrices, that a unitirradiance beam of natural light passing through a vertical linear polarizer is converted into a vertical P-state. Determine its...

The Jones vector for an arbitrary linearly polarized state at an angle θ with respect to the horizontal is Prove that this matrix is in agreement with the one in Table 8.5 for a P-state...

On examining a piece of stressed photoelastic material between crossed linear polarizers, we would see a set of colored bands (isochromatics) and, superimposed on these, a set of dark bands...

The specific rotatory power for sucrose dissolved in water at 20C ( 0 = 589.3 nm) is +66.45 per 10 cm of path traversed through a solution containing 1 g of active substance (sugar) per cm 3 of...

A Babinet compensator is positioned at 45 between crossed linear polarizers and is being illuminated with sodium light. When a thin sheet of mica (indices 1.599 and 1.594) is placed on the...

Linear light oscillating at 60 above the horizontal x-axis in the first and third quadrants passes through a quarter-wave plate with its fast axis horizontal. Explain why the light emerges as left...

Imagine that we have randomly polarized room light incident almost normally on the glass surface of a radar screen. A portion of it would be specularly reflected back toward the viewer and would thus...

Right-circular light passes through a λ/4 retarder whose fast axis is vertical. Describe the emerging polarization state. Did the polarization state shift one quarter of the way around...

A ray of yellow light is incident on a calcite plate at 50. The plate is cut so that the optic axis is parallel to the front face and perpendicular to the plane-of-incidence. Find the angular...

A narrow beam of light strikes the surface of a block of clear material and it is determined that the reflected light is totally polarized. If the total reflectance is 10% find the transmittance at...

Given that the critical angle for some transparent material in air is 41.0, determine its polarization angle.

The calcite crystal in Fig. P.8.34 is shown in three different orientations. Its blunt corner is on the left in (a), the lower left in (b), and the bottom in (c). The Polaroids transmission axis is...

Imagine a pair of crossed polarizers with transmission axes vertical and horizontal. The beam emerging from the first polarizer has flux density I 1 , and of course no light passes through the...

Linearly polarized light (with an irradiance of 200 W/m 2 ) aligned with its electric-field vector at +55 from the vertical impinges perpendicularly on an ideal sheet polarizer whose transmission...

One of the mirrors of a Michelson Interferometer is moved, and 1000 fringe-pairs shift past the hairline in a viewing telescope during the process. If the device is illuminated with 500-nm light, how...

A beam of linearly polarized light with its electric field vertical impinges perpendicularly on an ideal linear polarizer with a vertical transmission axis. If the incoming beam has an irradiance of...

Write an expression for an R-state lightwave of frequency propagating in the positive x-direction such that at t = 0 and x = 0 the vector E-field points in the negative z-direction.

Write an expression for a P-state lightwave of angular frequency and amplitude E 0 propagating along the x- xis with its plane-of-vibration at an angle of 25 to the xy-plane. The disturbance is zero...

Convert the following decimal numbers in the IEEE single precision format: (i) 25.25, (ii) 2000.22, (iii) 1, (iv) 0, (v) 1000, (vi) 8000, (vii) 10 6 , (viii) -5.4, (ix) 1.0 x 2 -140, (x) 1.5 x 10 9

To examine the conditions under which the approximations of Eq. (9.23) are valid: (a) Apply the law of cosines to triangle S 1 S 2 P in Fig. 9.11c to get (b) Expand this in a Maclaurin series...

(a) What is the biggest number that can be represented in the 8-bit 2s complement floating-point format with 4 bits for exponent and 4 for fraction? (b) What is the smallest number that can be...

(a) Use Shannon's expansion theorem around a for the function Y = ab'cd'e + a'bc'd'e + b'c'e + abcde so that it can be implemented using 4-variable functions. (b) Use the expanded function to show...

For the following circuit, find a minimum number of test vectors that will test all s-a-0 and s-a-1 faults at the AND and OR gate inputs. For each test vector, specify the values of A, B, C, and D,...

(a) How many logic blocks as shown in Figure 6-1(a) are required to create a 4-to-16 decoder? (b) Give the contents of the LUTs in the first logic block. Figure 6-1(a) X X Function QX D FF CE X2...

(a) Write Verilog code that describes the logic block shown in Figure 6-1(a). Use the following module: module Figure6_1a(X_in,Y_in,clk,CE,Qx,Qy,X,Y,XLUT,YLUT); input[1:4]X_in,Y_in; input CE,clk;...

The next-state equations for a sequential circuit with two flip-flops (Q 1 and Q 2 ), input signals R, S, T, and an output P are D 1 = Q 1 + = Q 2 R 1 Q 1 S D 2 = Q 2 + = Q 1 + Q 2 'T The output...

A collimated beam of microwaves impinges on a metal screen that contains a long horizontal slit that is 20 cm wide. A detector moving parallel to the screen in the far-field region locates the first...

(a) What are the conditions an SM chart must satisfy in order to realize it using single-address microprogramming with a counter, a ROM, and a multiplexer as in Fig 5-33? Figure 5-33: Microprogrammed...

Imagine two aperture screens arranged to produce two Fraunhofer diffraction patterns. One contains 8 very narrow closely spaced parallel slits, the other 16 such slits. All else being equal, compare...

Suppose we have 15 parallel long narrow slits in an opaque screen. Furthermore, suppose each slit is separated from the next by a center-to-center distance that is equal to 4 slit widths. Given that...

An opaque screen contains a rectangular hole 0.199 mm (along the z-axis) by 0.100 mm (along the y-axis). It is illuminated by light at 543 nm from a heliumneon laser. A big positive lens with a...

Consider the Fraunhofer diffraction pattern of a rectangular aperture 0.200 mm (in the y-direction) by 0.100 mm (in the z-direction). It is formed in 543-nm light from a heliumneon laser, on a screen...

Figure P.10.28 is the irradiance distribution in the far field for a configuration of elongated rectangular apertures. Describe the arrangement of holes that would give rise to such a pattern and...

In Fig. P.10.29a and b are the electric field and irradiance distributions, respectively, in the far field for a configuration of elongated rectangular apertures. Describe the arrangement of holes...

An angle has a value of 85. What is the angle in radians?

The seesaw in Figure P8.28 is 4.5 m long. Its mass of 20 kg is uniformly distributed. The child on the left end has a mass of 14 kg and is a distance of 1.4 m from the pivot point while a second...

We wish to use the 15-cm-diameter objective from an amateur telescope to form an image on a CCD of a distant star. Assuming a mean wavelength of 540 nm and a focal length of +140 cm, determine the...

Consider the function and first check that the exponents are unitless. Then show that the Fourier transform of E(t) is You might want to use the integral identity ,-! E(t) = Ege-i@ote-7/27 E(@) =...

A telescope having an objective lens with a diameter of 10.0 cm will be used to view two equally bright small sources of 550-nm light. (a) Determine the angular separation of the sources if they are...

Sunlight impinges on a transmission grating that is formed with 5000 lines per centimeter. Does the third-order spectrum overlap the second-order spectrum? Take red to be 780 nm and violet to be 390...

A grating has a total width of 10.0 cm and contains 600 lines/mm. What is its resolving power in the second-order spectrum? At a mean wavelength of 540 nm, what wavelength difference can it resolve?

Collimated light from a krypton ion laser at 568.19 nm impinges normally on a circular aperture. When viewed axially from a distance of 1.00 m, the hole uncovers the first half-period Fresnel zone....

Imagine a point source S a perpendicular distance Ï 0 from a circular hole in an aperture screen Σ. The screen is a distance r 0 in front of an axial observation point-P. Show that...

Design a hydraulic lift that could be used to move a car. Assume the input piston the person would push on has an area of 0.10 m 2 . If you want a force of 300 N applied by the person to lift a car,...

Explain how Archimedess principle can be used to measure a persons percentage body fat. Fat has a different density than other body tissue.

What will happen if water is poured on top of the mercury and ball bearing of Problem 78 such that the ball bearing is completely submerged in the water? Will the ball bearing (a) sink farther into...

Collimated red light (656.281 6 nm) from a hydrogen discharge lamp falls perpendicularly onto a transmission grating. The beam emerges forming a red line in the second-order spectrum at an angle of...

Compute the Fourier transform of the triangular pulse shown in Fig. P.11.11. Make a sketch of your answer, labeling all the pertinent values on the curve. Fig. P.11.11 f(x) -L +L

Given that F{(x)} = F(), introduce a constant scaling factor 1/ and determine the Fourier transform of (x/). Show that the transform of (-x) is F(-).

What is the rotational kinetic energy of the Earth as it spins about its axis?

The rectangular function is often defined as where it is set equal to 1/2 at the discontinuities (Fig. P.11.14). Determine the Fourier transform of Notice that this is just a rectangular pulse, like...

The cat in Figure 9.21 undergoes free fall due to the force of gravity. Explain why we did not consider gravity when we discussed how the cat in Figure 9.21 managed to land on its feet. Figure 9.21...

When a spinning figure skater pulls her arms close to her body (Fig. 9.11), she spins faster. If she then pushes her arms away from her body, her angular velocity decreases. Her rotational kinetic...

The displacement of a harmonic oscillator is given by y = 7.1 sin(48t), where the units of y are meters and t is measured in seconds. Give three values of t at which the oscillator has (a) Its...

A simple pendulum has a period of 2.5 s on the Earth. An astronaut then takes it to the surface of the Moon. What period does the astronaut measure there?

The cone of a loudspeaker oscillates with an amplitude of 2.0 mm. If the frequency is 2.5 kHz, what are the maximum velocity and the maximum acceleration of the cone? Assume the speaker cone moves as...

Under normal atmospheric conditions, the surface of the Earth is negatively charged. What is the direction of the electric field near the Earths surface?

Four point particles are located at the corners of a square (Fig. P17.15). The two particles on the left each carry a charge +Q. If the electric field at the center of the square is directed to the...

Two particles of charge Q and 5Q are located as shown in Figure P17.16. When a third charge is placed at the origin, it is found that the force on it is zero. Find a. Figure P17.16 ? y - L -L x. 5Q

An electron and a proton are a distance r = 7.5 10 -9 m apart. How much energy is required to increase their separation by a factor of two?

If the length of a wire is increased by a factor of 4, by what factor does the resistance change?

There is a potential difference of V 20 V across a resistor with R = 50. What is the current through the resistor?

If a current of 0.10 A flows through a resistor and the potential drop across the resistor is 1.5 V, what is the resistance?

Consider the configuration of resistors shown in Figure P19.108. Each connection can have a resistor that is disconnected or whose value is 5.0 or 10.0. To determine the value of each resistor or...

An electron is moving in the xy plane with its velocity along the -y direction. If the magnetic force on the electron is in the +z direction when B(vector) direction. If the magnetic force on the...

Faraday and many other scientists expected that there should be a certain symmetry between electric and magnetic phenomena. Is there a magnetic analog of electric charge? That is, is there such a...

In an electric circuit containing inductors, the largest induced voltage usually occurs just after a switch is opened or closed. Explain why.

An inductor has the form of a coil with 2000 turns and a diameter of 1.5 mm. The inductor is placed in a magnetic field perpendicular to the plane of the coil and increasing at a rate of 0.35 T/s....

Some resistors are made from a coil of wire. What is the best way to model the circuit behavior of such a resistor? Choose one answer and explain. (a) As an ideal resistor in series with an ideal...

Figure P23.2 shows the directions of the electric and magnetic fi elds associated with several different electromagnetic waves. What are the directions of propagation of these waves? Case 1 Case 2...

Find the RL time constant for decay of the current in the circuit in Figure 21.25B. Express your answer in terms of the values of the resistances R 1 and R 2 , and the inductance L. R2 R1

The human nose is very sensitive to certain molecules. For example, it can sense the presence of the chemical CH 3 SH (methyl mercaptan) at levels as small as 2 parts per billion. Another especially...

Consider the common expressions (a) Theres no such thing as a free lunch and (b) You cant even break even. Which of the laws of thermodynamics might these expressions refer to? Explain.

Bug breath. Insects do not have lungs or a blood circulatory system. Instead, a system of openings in the exoskeleton (spiracles) lead to branching tubes of decreasing diameter called trachea, the...

Describe a simple U-tube manometer.

Describe a differential U-tube manometer.

Describe a well-type manometer.

Describe an inclined well-type manometer.

Three surfaces of an instrument package are cooled by soldering half-sections of copper tubing to it as shown in Fig. 9.31. Compute the Reynolds number for each section if ethylene glycol at 77?F...

A hydraulic oil is flowing in a drawn steel hydraulic tube with an OD of 50 mm and a wall thickness of 1.5 mm. A pressure drop of 68 kPa is observed between two points in the tube 30 m apart. The oil...

Find the flow rate of water at 60?F in each pipe of Fig. 12.12. 0.3 ft/s 50 ft 50 ft 1.2 ft/s 30 ft 30 ft 50 ft 50 ft All pipes 25-in Schedule 40 0.3 ft/s 0.6 ft/s

A 2-kg brick has the dimensions 7.5 cm 15 cm 30 cm. The pressure the brick exerts on the ground when standing on its smallest face is a. 0.0178 Pa b. 0.0225 Pa c. 178 Pa d. 225 Pa

Which of the following isomeric carbocations is the most stable? CH,+ CH3 () (b) -CH3 CH3 () (d)

Write all sensible products of the reaction of each of the alcohols in Problem 31 with concentrated aqueous HBr. In Problem 31 OH () CH-CH-CH,O (b) CH;CHCH3 (c) CH;CH,CH,CH,OH OH (d) (CH),C, ()...

Give detailed mechanisms and final products for the reaction of 3-methyl-2-pentanol with each of the reagents that follow. (a) NaH (b) Concentrated HBr (c) PBr 3 (d) SOCl 2 (e) Concentrated H 2 SO 4...

What are the most likely product(s) of each of the following reactions? CH3 CH3 Conc. HI CH,CH,OH, H,SO, () HO (b) CH;CCH,OH CH3 CH,OH CH3 I Conc. H.SO, 180 () (d) CH, CH, H3

Suggest the best syntheses for each of the following ethers. Use alcohols or haloalkanes or both as your starting materials. () (b) () (d) () (f)

Propose syntheses of the following molecules, choosing reasonable starting materials on the basis of the principles of synthetic strategy introduced in preceding chapters, particularly in Section...

Give efficient syntheses of each of the following compounds, beginning with the indicated starting material. (a) trans-1-Bromo-2-methylcyclopentane, from cis-2-methylcyclopentanol (b) (c)...

Without consulting the Reaction Road Map on pp. 556 557, suggest a reagent to convert a general alkene, into each of the following types of compounds. H C=C

Give the expected product of reaction of 2-methyl-1-pentene with each of the following reagents. (a) H 2 , PtO 2 , CH 3 CH 2 OH (b) D 2 , Pd C, CH 3 CH 2 OH (c) BH 3 , THF then NaOH + H 2 O 2 (d)...

What are the products of reaction of (E)-3-methyl-3-hexene with each of the reagents in Problem 46? (a) H 2 , PtO 2 , CH 3 CH 2 OH (b) D 2 , Pd C, CH 3 CH 2 OH (c) BH 3 , THF then NaOH + H 2 O 2 (d)...

Compare the C2 C3 bonds in propane, propene, and propyne. Should they be any different with respect to either bond length or bond strength? If so, how should they vary?

Write the mechanism and final product for the reaction of 1-propynyllithium with trans-2,3- dimethyloxacyclopropane.

Show how the Heck reaction might be employed to synthesize each of the following molecules. doCH, () COCH3 (b)

The compound whose structure is H C C(CH 2 ) 3 Cl is best named (IUPAC) (a) 4-chloro-1-pentyne; (b) 5-chloropent-1-yne; (c) 4-pentyne-1-chloroyne; (d) 1-chloropent-4-yne.