UT_Austin_Invitational_2023_Optics EXAM

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Northwestern University *

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130-B

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Physics

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Apr 3, 2024

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University of Texas at Austin 2023 Invitational Optics B/C Exam Directions: • This is a class set, DO NOT WRITE • Write all answers on the answer sheets; any marks elsewhere will not be scored. If additional space is needed on a question, clearly mark the question number and your team number on the top left of the page and attach to your test. • There is no penalty for wrong answers. Answer as many questions as possible, even if you aren’t sure if you’re correct. For questions with parts that build on one another, points will be awarded for correct answers on parts regardless of previous part completion. • Units are required whenever giving a numerical answer. Don’t worry about significant figures. • Good luck on the test! Section 1 2 3 4 5 Total Total 20 24 17 15 51 127 Score Vidit Pokharna , vidit@gatech.edu Page 1 of 17

Fact or Fiction: The Optical Edition Circle T if true or F if false for the following statements 1.) (2 points) In the ray approximation of light, a ray is an actual physical line that represents the path of a light beam. T F 2.) (2 points) Light exhibits a dual nature, displaying characteristics of both a particle and a wave, depending on the context. T F 3.) (2 points) In the case of a concave mirror, if the object is placed between the focal point and the mirror, the image formed is virtual and magnified. T F 4.) (2 points) Due to atmospheric refraction, the stars seem to be higher in the sky than they actually are. T F 5.) (2 points) A plane mirror forms a real image of the objects placed in front of it. T F 6.) (2 points) A non-dispersive prism can separate white light into its component colors by re- fracting each color or wavelength of light at a slightly different angle. T F 7.) (2 points) Coherent light sources can produce interference patterns, while incoherent light sources cannot. T F 8.) (2 points) Incoherent light exhibits a high degree of monochromaticity, as compared to that of coherent light. T F 9.) (2 points) The human eye’s crystalline lens has the ability to change its focal length to focus on objects at varying distances, a phenomenon known as ”accommodation.” T F 10.) (2 points) Rod cells in the human retina are primarily responsible for color vision, while cone cells are responsible for detecting variations in brightness and contrast. T F Page 2 of 17

Optics Lingo Bingo Write the name of the term that best matches the definition 11.) (2 points) An optical phenomenon that occurs when light rays pass through the edges and center of a lens or mirror focus at different points, resulting in a blurred or distorted image. Answer: 12.) (2 points) A type of reflection that occurs when light reflects off a smooth surface and the reflected light rays are parallel. Answer: 13.) (2 points) A perfectly diffusive surface that reflects incident light uniformly in all directions, regardless of the angle of incidence Answer: 14.) (2 points) A phenomenon in color perception where two objects appear to have the same color under one light source but different colors under another. Answer: 15.) (2 points) A small depression in the retina that is responsible for sharp central vision. Answer: 16.) (2 points) Four principal points associated with a lens or mirror - the two focal points and the two principal points. Answer: 17.) (2 points) Pairs of colors that, when combined, cancel each other out to produce a grayscale color. Answer: Page 3 of 17

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18.) (2 points) A state in which atoms or molecules remain temporarily after being excited, before returning to their ground state by emitting a photon. Answer: 19.) (2 points) A tool for which the primary purpose is to reflect light or radiation back to its source regardless of the direction of the incident light. Answer: 20.) (2 points) The principle that states each point on a wavefront acts as a source of wavelets, which propagate forward at the same velocity as the original wave. Answer: 21.) (2 points) The area of the retina that contains the highest concentration of cones, responsible for high-acuity color vision. Answer: 22.) (2 points) The lens of the eye changes its shape through the process of accommodation, controlled by the action of the muscles. Answer: Page 4 of 17

Mix and Match Mayhem Provide the answers for the following questions 23.) (6 points) Pair the following materials with their respective indices of refraction. While the exact values may differ, select the value that is the closest match to the material’s index of refraction. 1.00, 1.3477, 1.36, 1.49, 1.52, 2.42 Air, Acrylic, Crown glass, Diamond, Ethanol, 10% Glucose Solution in Water a) Air (1 point) Answer: b) Acrylic (1 point) Answer: c) Crown glass (1 point) Answer: d) Diamond (1 point) Answer: e) Ethanol (1 point) Answer: f) 10% Glucose Solution in Water (1 point) Answer: 24.) (8 points) Answer the following questions on color theory. a) (1 point) In which model does mixing all three primary colors at full intensity yield black? Answer: Page 5 of 17

b) (1 point) In which model does mixing all three primary colors at full intensity yield white? Answer: c) (1 point) What color results from the mixture of cyan and yellow light? Answer: d) (1 point) What color results from the mixture of red and blue light? Answer: e) (1 point) What color results from the mixture of blue and green light? Answer: f) (1 point) What color results from the mixture of cyan and magenta light? Answer: g) (1 point) What color results from the mixture of red and green light? Answer: h) (1 point) What color results from the mixture of yellow and magenta light? Answer: Page 6 of 17

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25.) (3 points) Answer the name of the prism based on the picture. a) (1 point) Answer: b) (1 point) Answer: c) (1 point) Answer: Page 7 of 17

Chasing Shadows: A Light Odyssey The given arrow is the object. Trace to find the image, and draw it. As long as your image arrows are relatively in the correct position with a relatively correct height, you will receive full points. Additionally, state if it is a real or virtual image. 26.) (3 points) Answer: 27.) (3 points) Answer: Page 8 of 17

28.) (3 points) Answer: 29.) (3 points) Answer: Page 9 of 17

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30.) (3 points) Answer: Page 10 of 17

Mathemagical Optics: Where Numbers Meet Light Provide the answers for the following questions and box your answers so we know what your final answer is! 31.) (3 points) If a mischievous alien decided to give the Moon a makeover with a neon paint job, creating a disco ball effect visible from Earth, how long, to the nearest hundredth of a minute, would it take for the Earth to witness this interstellar ’glow up’ if the Moon is located 1 . 5 million kilometers away? Assume the alien’s paint reflects light at the speed of light, of course! Answer: 32.) (3 points) A beam of light strikes a mirror at an angle of incidence of 30 degrees made with a surface normal to the mirror surface. Calculate the angle at which the light is reflected off the mirror’s surface. Answer: Page 11 of 17

33.) (3 points) In a scenario where light travels (shown by the arrow) from a medium with a refractive index of n 1 = 1 . 67 to another medium with n 2 = 1 . 01, what is the critical angle θ , to the nearest hundredth of a degree, required to achieve total internal reflection? Answer: 34.) (3 points) How far from a convex mirror with a radius of curvature of 40 cm should an object be placed to ensure that the image formed is a third of the size of the object? Answer: Page 12 of 17

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35.) (3 points) Assume a certain concave, spherical mirror. Locate the image distance when the object distance is at the focal point. Answer: 36.) (3 points) Given a refractive index of 2 . 2 for glass and 1 . 0 for air, at what angle of incidence, to the nearest hundredth of a degree, will light in air be completely polarized when it passes into the glass? Answer: 37.) (3 points) At what distance d from a converging lens does it produce a virtual image, in terms of the focal length f ? Answer: Page 13 of 17

38.) (3 points) When a beam of white light transitions from air to flint glass at an incident angle of 23 . 7 degrees, what is the absolute angular separation, to the nearest thousandth of a degree, between the orange and violet components of the refracted light? The refractive indices for orange and violet light through flint glass are 1 . 665 and 1 . 698, respectively. Answer: 39.) (3 points) If you manage to polarize a laser pointer’s beam to create the ultimate game of ’chase the dot’ for your cat, emitting light at an intensity of 84 W m 2 , what would be the resulting intensity, to the nearest hundredth, after passing through a pair of stylish sunglasses, with their axis at an angle of 43 . 0 degrees to the laser beam’s polarization direction? Answer: Page 14 of 17

40.) (3 points) For a certain object emitting light in the visible spectrum, if the peak wavelength of the emitted radiation is 500 nm, what is the object’s temperature, to the nearest Kelvin? Answer: 41.) (3 points) A converging glass lens ( n = 1 . 62) has a focal length of 35 cm in air. What is its focal length, to the nearest centimeter, when it is submerged in an unknown liquid with a refractive index n = 1 . 42? Answer: 42.) (3 points) At what angle, to the nearest degree, should a polarizing filter be placed relative to the direction of incoming polarized light to decrease its intensity by 80%? Answer: Page 15 of 17

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43.) (3 points) A convex lens, made of a material with a refractive index of 1 . 5, has a curved surface with a radius of curvature of 20 cm on one side and 30 cm on the other side. What is the focal length of the lens, to the nearest centimeter? Answer: 44.) (3 points) An object is placed in front of a lens with a focal length of 25 cm. If the lens forms an image at a distance of 40 cm from the lens, what is the distance between the object and the lens, to the nearest centimeter? Answer: 45.) (3 points) For a certain medium with a refractive index of 1 . 6, what is the angle of incidence, to the nearest degree, at which light is completely polarized by reflection? Answer: Page 16 of 17

46.) (3 points) A beam of light enters an equilateral prism at an angle of incidence of 50 ◦ and emerges at an angle of 40 ◦ . What is the angle of deviation for the light passing through the prism? Answer: 47.) (3 points) Determine the total intensity ( I + I ′ ) of light transmitted by two polarizing filters, in terms of the original intensity, I 0 . The intensity I is for the first filter with its axis at an angle θ , and the intensity I ′ is for the second filter with its axis at an angle of 90 . 0 ◦ − θ . Answer: Page 17 of 17

UT_Austin_Invitational_2023_Optics EXAM

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