Republic of the Philippines Department of Education Regional Office IX, Zamboanga Peninsula 11/12 Z est for Progress Z P eal of artnership General Physics 2 Quarter 4 - Module 2 ELECTROMAGNETIC WAVES and LIGHT Name of Learner: Grade & Section: Name of School: 2 Module 2 ELECTROMAGNETIC WAVES and LIGHT What I Need to Know In the previous module, you have learned essential concepts about electricity and magnetism; this includes magnetic induction, Faraday's law, and Lenz's law. You were able to determine the similarities and differences between direct current and alternating current. You also have learned the concepts of LC circuits as energy passes from the conductor to the inductor. In this module, you are expected to learn the following: Content Standard: 1. Maxwell’s synthesis of electricity, magnetism, and optics 2. EM waves and light 3. Law of Reflection 4. Law of Refraction (Snell’s Law) 5. Polarization (Malus’s Law) 6. Applications of reflection, refraction, dispersion, and polarization Most Essential Learning Competencies: 1. Relate the properties of EM waves (wavelength, frequency, speed) and the properties of vacuum and optical medium (permittivity, permeability, and index of refraction. (STEM_GP12OPTIVb-12) 2. Explain the conditions for total internal reflection. (STEM_GP12OPTIVb-14) 3. Explain the phenomenon (STEM_GP12OPTIVb-16) of dispersion by relating to Snell’s Law. 4. Calculate the intensity of the transmitted light after passing through a series of polarizers applying Malus’s Law. (STEM_GP12OPTIVc-18) 5. Solve problems involving reflection, refraction, dispersion, and polarization in contexts such as, but not limited to, (polarizing) sunglasses, atmospheric haloes, and rainbows. (STEM_GP12OPTIVc-21) 2 What’s In 10 Activity 1. What’s the Word? Directions: Recall your previous lessons encountered when you were still in Junior High School about Electromagnetic Waves and Light. Can you still remember some of the important terms related to this topic? Below are jumbled letters of some of the essential terms that you will encounter in this module. Arrange the letters and write your answer on the blank provided. 1. 2. CTONREFILE ERSIONDISP 3. AIONRCTEFR 4. 7. GLEAN FO NCNCEIDEI AECURSPL CTIREFLEON ATOTL EANIRNTL TIOFLECNRE VELTHENGWA 8. UEQCYENFR 5. 6. 9. MECTROETICAGNEL VEWA 10. RIIOPOLANZAT -the bouncing of light rays when it hits a surface -separation of white light into different colors of light -bending of light rays when travelling from one medium to another -the angle formed between the incident ray and the normal line. -rays of light reflects in one direction only -a phenomenon when no light is refracted instead all light is reflected. -the distance measured from one crest of a wave to the next crest or from one trough to the second trough -the number of waves that pass a certain point in a specified amount of time -waves produced from the combination of electric and magnetic waves -process of transforming unpolarized light to polarized light What’s New 10 Activity 2. Mirror Reflect What do you think will happen to light as it strikes a smooth and shiny surface like a mirror? Perform the mirror experiment to learn substantial concepts about the reflection of light. Materials needed: Bondpaper, plane mirror, pencil, protractor, graphing paper and push pin. 3 Procedure: 1. On a bond paper, follow the set-up shown in figure 1. 2. Indicate the point of intersection of the perpendicular lines as point X. 3. Push the pin in any location on the left side of the paper. Indicate it as point Y. Connect points X and Y by drawing a Figure 1. Set-Up of the mirror experiment straight line. Refer to figure 2. 4. Position yourself on the right side of the mirror and push a pin indicated as point Z. D. Position point Z in a way that line XY and line XZ appear perpendicular to each other. 5. Use a protractor to measure the vertex angle formed between line XY and the vertical line. This angle is the angle of incidence ππ . 6. Use a protractor to measure the Figure 2. Lines and angles in the mirror experiment vertex angle formed between line ZY and the vertical line. This angle is the angle of reflection ππ 7. Repeat procedures 3-6 for five (5) different point Y positions and their corresponding point Z. Record your data in the table below. Table 2.Ζπ πππ Ζπ for Different Positions of the Pushpin Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 ππ ππ 8. Plot your data in the graph. 4 Guide Questions: 1. How does the measured value of the angle of incidence compare with the angle of reflection? 2. Based on your plotted graph, what can you infer between the relationship of π½π and π½π? What is it The Electric and Magnetic Fields Together Electromagnetic waves produced from accelerating electrons have both magnetic and electric field components. A changing magnetic field induces an electric field, and a changing electric field induces a magnetic field. Both the electric and the magnetic field oscillate perpendicular to each other and the propagating wave's direction. Figure 3.Electromagnetic wave with Magnetic and James Clerk Maxwell- described light as a Electric field components wave with components of both electric and Source: Science Learner’s Material Grade 10,p.146 magnetic fields. Hence, he developed equations that showed the relationship between electricity and magnetism. An electromagnetic wave with light as a component is a transverse wave produced by a vibrating electric charge. Since it is a wave, it possesses the characteristics of wavelength, frequency, and speed. All EM waves travel with a speed of 3 π₯ 108 in a vacuum and are denoted as c, the speed of light. Wave speed is π⁄π expressed in the equation π£ = ππ (equation 1) Where: v is the wave speed orc (speed of light) expressed in meter per second (m/s) f is the frequency in Hertz (Hz) π΄ is the wavelength in meters (m) As an EM wave enters a medium, various medium properties dictate how the EM wave propagates. Two of these properties are electric permittivity and magnetic permeability. Their relationship to light is given by the equation π£ =π = 1 √π’0π0 (equation 2) From this equation, you can identify that the relationship between the electric permittivity πΊπand magnetic permeability ππ is inversely proportional to light's speed. This means that either the electric permittivity or magnetic permeability increases in the material, the speed decreases, and vice versa. 5 Reflection of Light Did you get a similar drawing as shown in figure 4 in Activity 2 “Mirror Reflect”? Reflectionis the bouncing off of light rays when it hits a surface like a plane mirror. The ray of light coming from the source is the incident ray. The ray from the reflecting surface is the reflected ray, and the imaginary line perpendicular to the mirror surface is the normal line. From figure 4, the incident ray of light is the ray from the light source, the ray that Figure 4. Reflection of Light reflects from surface is the reflected ray and the line perpendicular to the mirror is the normal line. The incident ray, reflected ray, and the normal line all lie in the same plane. This is one of the laws of reflection. In Activity 2 “Mirror Reflect”, you found that “the angle of incidence is equal to the angle of reflection." This is the other law of reflection. In symbols: π½π =π½π (equation 3) a. Types of Reflection: a. Specular/ Regular Reflection -This reflects light on smooth surfaces such as mirrors or a calm body of water. b. b. Diffused/Irregular Reflection. This reflects light on rough surfaces such as clothing, paper, wavy water, and the asphalt roadway. Refraction of Light Refraction occurs when there is the bending of light rays when traveling from one medium to another. A measure of the optical density of a material is its index of refraction π . The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in the medium or, π= π ( π ππππ ππ πππβπ‘ ππ π£πππ’π’π) = π π£ (π ππππ ππ πππβπ‘ ππ πππππ’π) π£ Figure 5. Specular and Diffuse Reflection Source: Science Learner’s Material Grade 10,p.180-181 (equation 4) Figure 6 shows light refracts when passing through a material from a lower to a higher index of refraction π . This happens because light slows down as it enters a medium with a greater index of refraction. The bending of light occurs because of the change of its speed as it passes from one medium to another. 6 Figure 6. Refraction of light If π1isless thanπ2 (π1 < π2), the refracted ray bends towards the normal. But if π1 is greater than π2 (π1 > π2), then the refracted ray bends away from the normal. One of the laws of refraction states that “The normal line, the incident and the refracted ray all lie in the same plane." Snell’s law describes how a ray is refracted at the interface between two mediums of different indices of refraction. It is mathematically stated as: πππ¬π’π§Ζπ = πππ¬π’π§Ζπ (equation 5) where ππ is the refractive index of the first medium ππ is the refractive index of the second medium Ζπ is the angle of incidence Ζπ is the angle of refraction Dispersion of Light Sir Isaac Newton- used a glass prism to show that white light consists of different colors. Dispersion is a phenomenon in which a prism separates white light into its component colors. Dispersion of white light is caused by multiple refractions of the different colors of light. The angle of refraction depends on the index of refraction of the Figure 7. Dispersion of Light medium. Also, n depends on the wavelength. Note that the index of refraction is given as π = π, and speed is v=fπ΄. From these, we can infer that for a given medium, π£ n increases as wavelength decreases. We know that white light is dispersed in this order: red, orange, yellow, green, blue, indigo, and violet, with violet having the shortest wavelength and red the longest wavelength. For a given medium, n increases as wavelength decreases. Thus, n is greatest for violet and least for the red light. In the same way, violet light is bent more than red light. Sample Problem 1 A beam of light enters from water (with index of refraction of π1=1.33) to glass (with index of refraction of π2=1.52). The incident ray makes an angle of 40Λ with the normal. Find Ζπ and Ζπ. Solution: We have known values for the angle of incidence Ζ1 = 40Λ, π1=1.33, and π2= 1.52. Remember that the law of reflection states that Ζπ = Ζπ. Therefore,Ζπ = Ζπ = ππΛ 7 Figure 8. Reflection and refraction of light as it passes through water to a glass To find Ζπ, we use the Snell’s equation, ππ sin Ζπ = ππ sin Ζπ (1.33) (sin 40) π sin Ζπ Ζπ = sin−1 ( π )= sin−1 ( ) = 34.22Λ ππ 1.52 Therefore, the angle formed between Ζπ= 34.22Λ Since ππ is less than ππ (ππ < ππ), the refracted ray bends towards the normal and Ζπ > Ζπ. Total Internal Reflection occurs if light passes from a dense (with a higher refraction index) to a less dense medium (with a lower refraction index). Its angle of incidence ππ is greater than the critical angle ππ. The angle of incidence for which the angle of refraction is 90Λ is becomes the critical angle ππ shown in figure 6 (b). If the angle of incidence is greater than the critical angle, then the refracted ray will not exist, and all light rays will be reflected as shown in Figure 9 (c). The critical angle may be solved using: π =π sin−1 π2 π1 (equation 6) Figure 9. Total internal reflection Polarization of Light Polarization is a characteristic of all transverse waves. A simpler example of a transverse wave is a wave produced on a string. Moving the string upward and downward causes it to produce waves propagating in a single plane vertically. Light that propagates, in the same way, are linearly polarized waves. Moving the string in an upward and sideward motion produces waves with a random direction in different planes—light propagating in this manner are unpolarized waves. Light Figure 10. Unpolarized light passing through the polarizer and the analyzer. waves produced from a single 8 light source are polarized, while light from multiple sources such as the sun, flames, and incandescent bulbs produces unpolarized waves.. Unpolarized light can be linearly polarized using a polarizer; it permits only waves with a particular polarization direction to pass. If we place a second polarizing element along the path of an unpolarized beam of light, the first is called the polarizer, and the second is the analyzer. When unpolarized light with intensity π°πis incident on an ideal polarizer, the transmitted π° light's intensity is exactly half that of the incident unpolarized light π⁄π, no matter how the polarizing axis is oriented. When the linearly polarized light emerging from a polarizer passes through a second polarizer or analyzer, the analyzer's polarizing axis makes an angle Ζ with the first polarizer's polarizing axis. The intensity transmitted in the analyzer is given by Malus’s Law: π°π = π°πππππΖ (equation 7) Where π°π is the intensity of light that emerges through the analyzer. π°π is the transmitted intensity from the polarizer. Ζ is the angle formed between the transmission axes of the polarizer and the analyzer. Malus’s law applies only if the incident light passing through the analyzer is already linearly polarized. Sample Problem 2 An unpolarized light with an intensity of 100 W/π2passes through two polarizing filters, the polarizer then to the analyzer with transmission axes forming an angle of 30Λ. What is the intensity of the light as it passes through each filter? Solution: Remember that the intensity of the polarizer's transmitted light is exactly half that of the incident unpolarized light. Therefore, I0 100W/m2 π ⁄2 = 50 π/π¦ I1= ⁄ 2= To solve for the intensity of light emerging from the analyzer, use the Malus’s Law equation: I2 = I1cos2Ζ = (50 W/m2 ) ( cos2 30 ) = 37.5π/π¦π The intensity of light emerging from the analyzer is 37.5 π/π¦π Sample Problem 3 An unpolarized light with an intensity of 80 W/m2 passes through two polarizing filters. If the light that emerges from the analyzer has an intensity of 10 W/m2 , what is the angle between the two filters? Solution: To find the angle between the two filters, we need to develop an equation that describes I2 πππ I0 since we have known values for both. 9 I I Remember that I1 = 0⁄2, substitute I1 in Malus’s Equation with 0⁄2. (Malus’s Equation) I2 = I1cos2Ζ I I (Substitute 0⁄2 to I1 ) I2 = 0⁄2 cos 2Ζ Finally, we get the formula for Ζ, Ζ = cos−1 √ 2I 2 I0 W =cos−1√ 2 (10 ) m2 80W/m2 = cos−1√π. 25 = cos−1 (0.5) = 60Λ The angle between the two filters is 60Λ What’s More 10 Activity 3. Break the Code For you to break the code, match the problems in the rectangles with their answers in oblongs. Write the letter of your answer in the blank before each item. (2 points each) 1. 2. 3. 4. 5. CODE: An incident ray of light passing through the air (n=1.0) strikes the crown glass's surface (n=1.52) at an angle of 35Λ. What will be the angle of refraction? If the refraction index of plexiglass is 1.51 and the refraction angle is 20Λ for a ray of light traveling from the air (n=1.0). What is the angle of incidence? Light striking a mirror makes an angle of incidence of 45Λ. What is the angle of reflection? An unpolarized light with an intensity of 150 W/π2passes through the first polarizer. What is the intensity of light that emerges through it? An unpolarized light with an intensity of 120 W/π2passes through the polarizer then to the analyzer with transmission axes forming an angle of 30Λ. What is the intensity of the light as it passes through the analyzer? ! 10 45Λ 45 W/π2 61Λ 22Λ 30Λ 52 W/π2 13Λ 75 W/π2 125 W/π2 60Λ What I Have Learned 10 Activity 4. Make it Right! Great! You’re almost done with the module. To summarize what you have learned from the lesson, underline the word inside the parenthesis that makes the statement correct. 1-2. Electromagnetic waves are (transverse, longitudinal) waves that can propagate with or without a medium. The medium wherein EM waves propagate has properties such as electric permittivity and magnetic permeability, which is both (directly, inversely) proportional to light's speed. 3-4 When light cannot get out of the boundary between transparent media, an interesting phenomenon occurs called total internal reflection. In this event, the incident angle must be (greater, lesser) than the critical angle and all light rays are (refracted, reflected). 5-6. The separation of white light into seven component colors of light, when allowed to pass through a glass prism, is called (polarization, dispersion). Snell's Law can explain this phenomenon. Since the index of refraction depends on the wavelength of the color of light, then the refractive index is greater for (orange, indigo) light. 7. According to the law of reflection, the angle of incidence is (greater than, lesser than, equal to) the angle of reflection. 8-10 Electromagnetic waves having a definite direction relative to the direction of the wave's propagation, like standing waves on a string, are said to be (polarized, unpolarized). Unpolarized light waves pass through two polarizing filters. The first one is called the polarizer, which reduces the light intensity in half, while the latter is called the (polarizer, analyzer, filter). (Malus’s Law, Snell’s Law) quantifies the light intensity that emerges from these series of polarizing elements. What I Can Do 20 Activity 5A. Label Me! Directions: The diagram shows a light ray path as it travels from one medium to another. Label what is indicated in the diagram by writing your answer on the blank. Choose your answer from the box. angle of incidence greater than incident ray reflected ray refracted ray normal line angle of refraction less than angle of reflection 11 Activity 5B. Completion The first column shows the path of a light ray as it passes through two different media. Fill in the missing values by choosing from the box below. Media 1. Air to π1 1.00 Ζ1 25Λ π2 Ζ2 11.34Λ 51Λ 1.58 42Λ 30Λ 1.52 diamond 2. Ethyl alcohol to light flint glass 3. Water to 1.33 crown glass 4. Water to ice 5. Air to zircon 6. Ice to 1.33 1.00 1.31 1.31 40Λ 54.6Λ 23Λ 19.6Λ 45Λ plexiglass 0.47 1.36 2.15 1.84 25.94Λ 23.37Λ 12 1.92 1.51 34.85Λ 22.63Λ An unpolarized beam of light with intensity πΌ0 passes through two polarizing elements. Determine the missing values in the table by choosing from the box. Light beam 1 2 3 4 5 6 60Λ 30Λ πΌ0 (W/m2) 220 150 75 180 60 πΌ1 (W/m2) 110 45.0 37.5 90.0 30 90 40Λ 58 29.60 πΌ2 (W/m2) 73.8 39.7 40.1 9.40 Ζ 20Λ 43Λ 55Λ 15Λ 75 65 28.0 35Λ Assessment 15 Directions: Read and analyze each item carefully. Write the letter of your answer on the blank provided. 1. Which of the following is NOT true about electromagnetic waves? A. A combination of electric and magnetic fields produces Electromagnet waves. B. Electromagnetic waves can travel through a medium. C. All electromagnetic waves travel with a speed of 2 π₯ 108 π⁄π in a vacuum D. Electromagnetic waves possess the characteristics of wavelength, frequency, and speed. 2. It states that the angle of incidence is equal to the angle of reflection. A. Law of Refraction C. Snell’s Law B. Law of Reflection D. Malus’s Law 3. What do you call the reflection of light on rough surfaces? A. Regular Reflection C. Diffused Reflection B. Specular Reflection D. Both A and B 4. Which of the following is an example of specular reflection? A. Reflection on the surface of the water B. Mirror reflection C. Light striking a cemented road D. Light striking a sprite bottle. 13 5. A ray of light goes from medium A to B with an angle of incidence at 40Λ and an angle of refraction at 30Λ. How will you compare the speed of light? A. The speed of light in B is less than that in A B. The speed of light in B is the same as that in A C. The speed of light in B is greater than that in A D. Both A or B 6. An incident ray of light travels from air to water, as shown in the figure. Which is the refracted ray? 7. You are looking at stones at the bottom of a clear and still pond. Your line of vision is directly above the water. You observed that the stones appear closer to the surface than it actually is. Which of the following statements best explain your observation? A. Light entering the water is dispersed. B. Specular reflection is observed on the surface of the water. C. Light reflects in a different direction as it strikes the surface of the water D. Light bends as it enters through the water. 8. A beam of light enters from water (index of refraction ππ =1.33) to glass (index of refraction ππ=1.52). Which of the following statements is true to this situation? A. All light rays reflect from the surface of the glass B. Light refracts away from the normal since ππ < ππ C. Light refracts towards the normal since ππ < ππ D. The angle of refraction is greater than the angle of incidence. 9. The following are the conditions for total internal reflection to occur exceptA. The index of refraction of the first medium should be lesser than the second medium. B. The incident angle must be greater than the critical angle. C. All light rays are reflected. D. None of the light rays are refracted. 10. A ray of light travels from the air (n=1.00) to water (n=1.33) with an angle of incidence of 45Λ with respect to the normal, what is the angle of refraction? A. 32.1Λ B. 28.9Λ C. 25.5Λ D. 35.1Λ 11. It is the phenomenon that explains the appearance of a rainbow. A. Refraction B. Reflection C. Dispersion D. Polarization 12. The dispersion of white light through multiple refractions of its component colors depends on its wavelength and the index of refraction of the medium. What happens to the index of refraction of a given medium if wavelength increases? A. Increases B. decreases C. remains the same D. either B or C 13. A beam of light that is composed of many rays having random polarization directions. A. Polarized light C. Filtered Light B. Unpolarized light D. Unfiltered light 14 14. An unpolarized light with the intensity πΌ0 passes through a polarizer. What is the intensity of light πΌ1that emerges through it? A. One-half of πΌ0 C. Twice the πΌ0 B. ¼ of πΌ0 D. Equal to πΌ0 15. An unpolarized light passing through a polarizing filter achieved an intensity of 50 π€⁄π 2. What will be its intensity after passing through the second filter oriented at an angle of 40Λ from the first one? A.1.3 π€⁄π 2 B. 29.3 π€⁄π 2 C. 2000 π€⁄π2 D. 90.0 π€⁄π2 Additional Activities 10 Activity 6. Problem Solving Directions: Solve the following problems and show your solution in the space provided. 1. Snell’s Law: An incident ray of light passes through two media, oil, then to water at an incident angle of 38Λ. If refractive indices are 1.45 and 1.33, respectively, what will be the angle of refraction? To what direction will the light ray bend with respect to the normal line as it passes through water? (5 points) 2. Malus’s Law: An unpolarized light with an intensity of 150 W/π2passes through the polarizer then to the analyzer with transmission axes forming an angle of 24Λ. What is the intensity of the light as it passes through each polarizing filter? (5 points) 15 References Books: Physics Science and Technology Textbook for Fourth Year, Reprint Edition,2007,2009 Science Learner’s Material Grade 10 pages 146,175, 180-181 Science Learner’s Material Grade 7 page 180 Electronic Resources: Polarization is a characteristic of all transverse waves. Retrieved from https://www.coursehero.com/file/77431374/Polarization-5ppt/ When the linearly polarized light. Retrieved from https://byjus.com/jee/malus-law/ Malus's law. Retrieved from https://physicsmax.com/polarizing-filters-4831 Development Team Region IX Hymn OUR EDEN LAND Writer: Juvelyn B. Pantanosas, T-I Editors: Mohamad Ali E. Ramber, MT-I Reviewer: Mila P. Arao, EPS Illustrator: Layout Artist: Management Team: Here the trees and flowers bloom, Here the breezes never gently blow, Here the birds sing IX... merrily, And liberty forever stays, DANNY B. CORDOVA EdD, CESO VI SDS-Pagadian City MA. COLLEN L. EMORICHA, EdD, CESE ASDS MA. MADELENE P. MITUDA, EdD EPS-LRMDS MILA P. ARAO EPS-Science 16 Golden beams of sunrise and sunset, Are visions you’ll forget. Oh! That’s Region Hardworking people abound, Every valley and dale Zamboangenos, Here the Badjaos Tagalogs, swam the seas, Bicolanos, Here the Samals live in Cebuanos, Ilocanos, peace, Subanens, Boholanos, Illongos, Here the Tausogs All of them are proud thrive so free, and true With the Yakans in Region IX our unity. Eden Land. Gallant men And Ladies fair, Region IX, our Eden Linger with love and Land. care,