Homework Assignment Light Waves

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Started on Thursday, 19 November 2020, 4:12 PM State Finished Completed on Thursday, 19 November 2020, 8:56 PM Time taken 4 hours 43 mins Marks 6.87/9.00 Grade 76.30 out of 100.00 Question 1 Correct Mark 1.00 out of 1.00 When a beam of unpolarized light is sent through two polarizing sheets, the transmitted intensity is 38.6 percent of the initial intensity. What is the angle between the polarizing directions of the two sheets? Answer: [ 0.498 }/ rad Half the initial intensity is transmitted through the first sheet. The intensity transmitted through the second sheet is Tiran _ (.5) cos® () Iy Solving for 6, The correct answer is: 0.498 rad Marks for this submission: 1.00/1.00. Question 2 Correct Mark 0.90 out of 1.00 A beam of unpolarized light (in air) strikes a flat glass surface and is partially reflected and partially refracted. When the angle of incidence is 53.8 degrees, the reflected beam is 100% polarized. What is the angle of refraction? Answer: [ 36.2 }/ degrees When the reflected beam is completely polarized, the angle of incidence must be equal to Brewster's angle and the angle between the refracted and reflected beams is 90°, therefore the angle of refraction is 90° — 8 = 90 — 53.8 degrees. The correct answer is: 36.2 degrees Marks for this submission: 1.00/1.00. Accounting for previous tries, this gives 0.90/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 1/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Question 3 Correct Mark 0.70 out of 1.00 A beam of partially polarized light can be considered to be a mixture of polarized and unpolarized light. Suppose a beam of partially polarized light is sent through a polarizing filter. The polarization direction of the filter can be changed by rotating it. As the filter is rotated through 360 degrees, we observe that the transmitted intensity varies from some minimum value ;i to a maximum value of 9.7 times |y,;,. What fraction of the intensity of the original beam is associated with polarized light? Answer: ‘ 0.813 ]\/ The incident beam has initial intensity lun + Ipol. The transmitted intensity is minimum when the polarizing direction of the filter is perpendicular to the polarized portion of the incident beam. At this point, none of the polarized light is transmitted, therefore |, represents 50% of the intensity of the unpolarized portion: Iy, = 2(Imin) - The transmitted intensity is maximum when the filter is parallel to the direction of polarized beam. At this point, all of the polarized light is transmitted in addition to I,,i, due to the unpolarized portion. Therefore the difference between the maximum and minimum intensitites is equal to the intensity of the polarized portion of the beam: Ipol = Imam - Imin = (97 - l)Imz The total initial intensity of the beam before passing through the polarizer is Lot = Ly + Ipot = 2(Ipin) + (9.7 — )i, = (9.7 + 1) L1, The fraction of the beam which is polarized is The correct answer is: 0.813 Marks for this submission: 1.00/1.00. Accounting for previous tries, this gives 0.70/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 2/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Question D Complete Not graded Three polarizing sheets are stacked on top of each other. Their polarization directions (relative to an arbitrary reference line) are 0, 45, and 90 degrees. (a) Consider the fraction of initially unpolarized incident light that would be transmitted through the stack. Does the order in which they are stacked affect your answer? Explain briefly. (b) Now suppose the first and third sheets are fixed in place, with polarization directions of 0 and 90 degrees respectively; the middle sheet can be rotated. How does the intensity of transmitted light vary qualitatively as you rotate the middle sheet from 0 to 90 degrees? a. Yes. Because if 0 and 90 are beside one another it will be 100 percent polarized. But if another sheet is introduced in the middle that would allow some light to pass through the system. b. As you increase the angle of the second sheet/ middle sheet the more the light will be blocked off. Because if the middle sheet is parallel to the first or third sheet it will be 100 percent polarize. (a) Yes. The 45 degree sheet must be placed between the other two. If the 90- and zero-degree sheets are adjacent, they would block all light. (b) The transmitted intensity would be zero at 0 degrees (where sheet 2 is perpendicular to sheet 3), increase to a maximum at 45 degrees and decrease to zero at 90 degrees (where sheet 2 is perpendicular to sheet 1). https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 4/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Question 6 Correct Mark 1.00 out of 1.00 In the diagram below, five cases labeled A through E are illustrated. In each case, white light is incident upon the interface between two transparent media (labeled 1 and 2), and the red and blue refracted rays are shown with appropriate colours. Given that the refractive index of medium 2 is greater than that of medium 1 (n, > n4) which of the cases shows normal dispersion? A B C 1 1 ; 2 R 2 2 white light | 1 2 2 Select one: A Cross out « B cross out C cross out D cross out E cross out Your answer is correct. Normal dispersion requires that the group velocity is less than the phase velocity and so: dw dw _ w dk k Hence as w increases the phase velocity will decrease which means that the refractive index will increase. Since blue light has a higher frequency than red light this will mean that it will see a higher refractive index and so will get bent more by refraction. Since the refractive index of medium 2 is higher the rays must be bent towards the normal to the surface and must not go past the normal to the surface. The only option which fulfills all these requirements is A. The correct answer is: A Marks for this submission: 1.00/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 5/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Question 8 Correct Mark 1.00 out of 1.00 White light is incident on a block of glass that has index of refraction n = 1.816 for violet light and n = 1.800 for red light. The thickness of the block is L = 42 cm. If the angle of incidence is 43 degrees, what is the distance x between the violet and red rays when they emerge from the glass? Take the index of refraction of air to be 1.00. —L — Answer: [ 0.176 j\/ cm The index of refraction for air is 1.00. Calculate the angle of refraction for red light and blue light: . sin 01 Sin 6y yeq = 9 nr and . sin 6, S111 92,blue — T The distance separating the to rays when they exit the glass is... x = Ltan @y ,cq — Ltan 0; ppye The correct answer is: 0.177 cm Marks for this submission: 1.00/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 7/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Question 9 Correct Mark 1.00 out of 1.00 Refer to the previous problem about the glass block. What is the angle between the paths of the red and violet rays when they emerge from the glass on the right side of the block? Answer: [ 0 ]\l degrees Because the sides of the block are parallel the bending done by the refraction at the first side is exactly undone by the bending due to refraction at the other because the indices of refraction are the same at both interfaces for any particular colour. Only inside the block itself do the different colours have different angles and this is because they have only undergone one refraction upon entering the glass. The correct answer is: 0 degrees Marks for this submission: 1.00/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 8/10

11/16/23, 6:30 PM Homework 9: Light Waves: Attempt review Marks for this submission: 1.00/1.00. Accounting for previous tries, this gives 0.60/1.00. Question 11 Incorrect Not graded The relationship between angular frequency and wavenumber for a deep water wave is: w=/gk where g is the acceleration due to gravity. If the phase velocity of a particular wave is 4.7 m/s what is the group velocity of the wave? Answer: ‘ 0.652 ]@m/s The phase velocity is given by: and the group velocity is given by: The correct answer is: 2.35 m/s https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=6523333&cmid=4375411 10/10