Water a) 48 o b) 53 o c) 41.5 o d) 44 o. Glass. PHYSICS 223 Exam-2 NAME II III IV

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1 PHYSICS 3 Exa- NAME. In the figure shown, light travels fro aterial I, through three layers of other aterials with surfaces parallel to one another, and then back into another layer of aterial I. The refractions (but not the associated II III IV reflections) at the interfaces are shown..a Rank the aterials according to the index of refraction, greatest first. I I a) II, IV, I, III b) II, I, IV, III c) IV, III, I, II d) IV, I, III, II.B Circle the expression(s) that is (are) right a) In the figure above, assuing that the incident angle reains the sae, if the layers II and IV were interchanged, then the refracted angle would increase. b) In the figure above, assuing that the incident angle reains the sae, if the layers II and IV were interchanged, then the refracted angle would decrease. c) In the figure above, assuing that the incident angle reains the sae, if the thickness of layer III is reduced to zero, then the refracted angle would increase. d) In the figure above, assuing that the incident angle reains the sae, if the thickness of layer III is reduced to zero, then the refracted angle would decrease. e) All the expressions above are incorrect.. A ray of light falls on a rectangular glass block (n g =.5) that is alost copletely suberged in water (n w =.33) as shown in the figure.a Find the axiu angle ax at which total internal reflection at the water-glass interface still occurs. Water a) 48 o b) 53 o c) 4.5 o d) 44 o Glass

2 .B Would total internal reflection occur at the vertical interface for the value of ax found in part A above if the water were reoved? Circle your answer. ANSWER: YES NO 3. A polarizer is rotated at a rate of revolution per second between a siilar pair of stationary crossed polarizers (the stationary polarizers have their transission axis oriented perpendicular to each other.) stationary 3A. The intensity of the eergent bea (after passing the 3 polarizers) will change at a frequency equal to (in cycles/sec) Z rotating stationary I Y Incident bea of rando polarization X a) b) 8 c) 3 d) 4 3B. At the instant when the transission axis of the rotating polarizer akes 60 degrees with the first polarizer, the fraction of light s initial intensity transitted by the syste is a) 8 b) 3 3 c) 6 d) A The laws of refraction and reflection are the sae for sound as for light. The speed of sound in air is 340 /s and in water it is 50 /s. If a sound wave approaches a plane water surface at an angle of incidence of, what is the angle of refraction? a) 49.3 b).7 c) 67.4 d) 4B A layer of ethyl alcohol (n =.36 ) is on top of water (n =.333). At what angle relative to the noral to the interface of the two liquids is light totally reflected? a) 78 b) 88 c) 68 d) 58 e) The critical angle is undefined. 5. 5A A ray passes fro air (n a =) into water (n w =.33), striking the surface of the water with an angle of incidence of 45 o. Which of the following four quantities change as the light crosses the air-water interface: () wavelength, () frequency (3) phase velocity (4) direction of propagation,

3 a) and, only b), 3, and 4, only c), 3, and 4, only d) 3 and 4, only e),, 3, and 4 5B Calculate the fraction of light energy reflected fro an air-water interface at noral incidence. a) 4% b) % c) 0.3% d) % 6. 6A A glass surface (n g =.5) has a layer of water on it (n w =.33). Light in the glass is incident on the glass-water interface. Find the critical angle for total internal reflection. a) 5 b) 59 c) 4 d) 48 6B The figure below shows two plane irrors that ake an angle q with each other. The angle between the incident and reflected ray is a) b) c) 3 d) / e) (/3) 7. The figure shows the profile of an incident wave at t=0. Air Glass Incident wave 7.A Sketch the profile of the transitted and reflected wave at t=0 Air Glass

4 7.A Sketch the profile of the transitted and reflected wave at t=t/4 (where T is the period of the wave). Air Glass 8. The figure below shows red and green light incident fro air. The thickness "L" of the thin fil is unknown. red = 650 n L A B green = 50 n n =.0 n 3 =.5 8A 8B Which of the following expression is correct a) The frequency of the red bea is higher when travels inside the fil when copared to its frequency in the air b) The frequency of the green bea is higher when travels inside the fil when copared to its frequency in the air c) The tie it takes for the green bea to travel fro A to B and return to A (inside the fil) is nuerically equal to 4L/c d) The green bea incident on the interface "B" will experience 80 degrees phase shift upon reflection. Which of the following expression is correct a) The green bea incident on the interface "B" will experience 80 degrees phase shift upon reflection, but the red bea will experience no phase shift.

5 b) In the case of the red light: If the fil were very sall (L< 0. red ) the beas reflected fro the interfaces "A" and "B" will interfere destructively. c) In the case of the green light: If the fil were very sall (L< 0. green ) the beas reflected fro the interfaces "A" and "B" will interfere constructively. d) In the case of the green light: If the fil were very sall (L< 0. green ) the beas reflected fro the interfaces "A" and "B" will always interfere constructively regardless of the value of n A White light, with a unifor intensity across the visible wavelength range of 400 n to 690 n. Is perpendicularly incident on a water fil of index of refraction n=.33 and thickness L=30 n, that is suspended in air. At what wavelength does the light reflected by the fil look brightest to an observer? a) 475 b) c) 657 d) 567 n 9B. The figure shows the reflection of light fro a thin fil of thickness L and index of refraction n surrounded by air (the rays are drawn tilted for clarity). What is the phase difference between the rays 3 and 4? 3 4 L a) nl b) nl c) L d) A In order to calculate the force an ideal gas exerts on the wall of a container, we assue that each olecule transfers oentu of agnitude o v x when it collides with a wall perpendicular to the x-axis. To calculate the force that each olecule exerts on the wall we can also assue that the tie interval between collisions in a cube of side length d is a) d v x b) d v x c) v x 0B An ideal gas is coposed by 3.7 x 0 7 onoatoic particles which fill a vessel of volue V= 3 x 0 x 5, exerting a pressure of P = atosphere at T= 300 K. What of the following expressions is correct? a) In the sae vessel and at the sae teperature of 300K, 3.7 x 0 7 diatoic particles will exert a pressure of P = atospheres. d d) d v x e) v x d

6 b) In the sae vessel and at the sae teperature of 300K, 3.7 x 0 7 diatoic particles will exert a pressure of P = atosphere. c) In the sae vessel and at the sae teperature of 300K, 3.7 x 0 7 diatoic particles will exert a pressure of P = 0.5 atospheres. d) In the sae vessel and at the sae teperature of 300K, 3.7 x 0 7 diatoic particles will exert a pressure greater than atosphere, but there is not enough inforation to calculate the exact pressure. e) In the sae vessel and at the sae teperature of 300K, 3.7 x 0 7 diatoic particles will exert a pressure lower than atosphere, but there is not enough inforation to calculate the exact pressure. The figure shows a horizontal planks of length L=50 c, and ass M= Kg, pivoted at one end. The planks is also supported by a spring at 3/4 of its length, as shown in the figure; the spring constant has a value of k=0 N/c. The spring is neither copressed nor stretched when the plank is horizontal. Assue that the plank L/4 undergoes sall aplitude oscillations? 3L/4.A Draw the corresponding free body diagra for the plank and indicate the agnitude of the torque (calculated around the pivot point) produced by each of the forces when = 0.0 radians. k 3L/4 L/4 Torque : Torque 3: Torque :.B Consider the sae echanical syste described in question # above. a) 6.5 b) 9.0 c) 5.8 d) 0.75

7 SOME HELPFUL FORMULAS Hertz = Hz = oscillation per second n = 0-9, = 0-6 = 8.85 x 0 - F/ c= 3x0 8 /s Angle in radians (radian) = length/radius = l / R Identity: E COS ( A ) E COS ( B ) Waves y = A COS(kx-t +) A = aplitude, ( t ) = phase of the otion, is the phase constant, and is the angular frequency. Speed: v f T (Period) f f (angular frequency) T A B A B E COS ( ) COS ( ) k _ Waves traveling along a string: v = (T/ ) / Snell s law n SIN n SIN _ Index of refraction: c n Doppler Effect: V f observer f source V sound sound v v observer source _ B Beat frequency: Let p p 0 COS ( ) t p 0 COS ( t ) p 0COS ( t ) COS ( ) blue red _ Electroagnetic waves: E B y z E COS ( kx wt ) B COS ( kx wt ) E y B z x t Poynting vector S 0 E B c E x B Magnitude of the Poynting vector S ce 0 Average: S ce 0 n() Brewster angle Angle reflection + angle refraction = 90 o Phase shift: k THIN FILM INTERFERENCE Condition for MAX reflection (case a slab of thickness L and index of refraction n surrounded by air) 0 L N N,3,5,... n L V First Law of Therodynics U = Q W

8 Poynting vector S ve _ Diffraction Grating Angular location of the first iniu of intensity (around the zero-order axiu) n d SIN( in ) = where n is the nuber of slits participating in the diffraction. RESOLVING POWER Diffraction Grating R= n, where is the required iniu difference between two wavelengths in order to distinguish the using the grating n is the nuber slit in the grating. is the order of the axiu intensity ( =,,3, ). Ideal Gas PV = nrt, R = 8.3 x 0-3 J/ol K PV=NkT, k =.38 x 0-3 J/K Absolute Teperature Scale or Kelvin Scale T = t Celsius K