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Physics – Light

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    Study Guide Physics – Light 1. Diffraction Thomas Young’s double - slit experiment showed that light behaves like a wave . When light waves overlap, they can interfere with each other — either reinforcing or canceling out. One important wave behavior is diffraction . Diffraction happens when a wave spreads out as it passes through an opening or bends around an obstacle. Why diffraction is easy to notice with sound but not light Diffraction depends strongly on wavelength . • Sound waves have long wavelengths, so they diffract easily. This is why you can hear sound through a doorway or even around corners. • Light waves have extremely short wavelengths. Because of this, light diffraction is much harder to observe unless the opening is very small. 1. Single - Slit Diffraction When light passes through a single narrow slit , it does not form just a simple bright spot. Instead, it creates a pattern of bright and dark fringes on a screen. This pattern occurs because of both diffraction and interference . Imagine the slit is wide enough to allow many wavelets to pass through. Each point across the slit acts as a source of waves, and these waves interfere with one another.

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    Study Guide 1. Analysis of Dark Fringes (Minima) In Figure 1, light rays from different points across the slit travel to a point P on a distant screen. • Consider rays from points A and B . • The path length from A to P is half a wavelength longer than from B to P . • Because of this half - wavelength difference, the two waves destructively interfere and cancel each other out. This same cancellation happens for all wavelets across the slit: • Every wave from one part of the slit has a partner wave from another part that cancels it. • Since the waves cancel in pairs, point P becomes a dark fringe (minimum) . Because point P is far from the slit, triangle ACD is nearly a right triangle. Using geometry, we obtain the condition for the first dark fringe: where: • ( λ ) is the wavelength of light • ( w ) is the width of the slit

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    Study Guide Whenever the path difference equals a whole number of wavelengths , complete cancellation occurs and a dark fringe appears. 2. Partial Reinforcement and Bright Fringes In Figure 2, the slit is divided into three equal regions . • Waves from two regions cancel each other through destructive interference. • Waves from the remaining region reinforce each other . Because only part of the slit contributes constructively, the result is partial reinforcement , not maximum brightness. This produces a secondary bright fringe . For this case, the angle of the fringe is given by: These secondary bright fringes are much weaker than the central bright fringe.

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    Study Guide 3. Intensity Pattern of Single - Slit Diffraction Figure 3 shows how light intensity changes with angle . Key observations: • The central maximum is the brightest and widest region. • This happens because all wavelets interfere constructively at the center. • On either side of the center, the intensity decreases. • Alternating dark and weak bright fringes appear symmetrically. 2. Diffraction in the Double - Slit Experiment When using two slits , it is impossible to observe only the double - slit interference pattern. Why? • A double slit is actually two single slits . • Each slit produces its own diffraction pattern .

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    Study Guide As a result: • The observed pattern is a combination of double - slit interference and single - slit diffraction . • The diffraction pattern acts like an envelope that controls the brightness of the interference fringes. 2. Characteristics of Light Scientists have studied light for centuries, and our understanding of it has changed over time. 1. Early Ideas About Light • Isaac Newton believed that light was made of tiny particles. His particle theory helped explain how light reflects from mirrors and refracts when it passes from air into water. • At the same time, Christiaan Huygens proposed that light behaves like a wave . His wave theory also successfully explained reflection and refraction. Later, in the late 1800s: • James Clerk Maxwell predicted the existence of electromagnetic waves . • Gustav Ludwig Hertz experimentally confirmed these waves and showed that they travel at the speed of light . Because of this work, light is now understood as: • a wave • a particle • a form of electromagnetic radiation

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    Study Guide 2. The Dual Nature of Light Today, scientists accept that light has a dual nature . • In some experiments, light behaves like a wave . • In other experiments, it behaves like a particle . Because of this, asking whether light is only a wave or only a particle is not useful. Instead, it is better to think of waves and particles as models that help explain different behaviors of light. 3. Electromagnetic Spectrum Maxwell’s equations unified electricity, magnetism, and optics into one theory. Light is just a small part of a much larger range of electromagnetic waves called the electromagnetic spectrum . Important points: • Visible light is the only part of the spectrum our eyes can detect. • Wavelengths are commonly measured in:

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    Study Guide ○ nanometers (nm) , where (1 \ text{ nm} = 10^{ - 9} \ text{ m}) ○ angstroms (Å) , where (1 \ text{ Å} = 10^{ - 10} \ text{ m}) • The visible spectrum ranges: ○ from violet (shortest wavelength) ○ to red (longest wavelength) 4. Speed of Light Light travels extremely fast — about: [3 .15 × 10 8 m/s] Because of this enormous speed, it was very difficult to measure accurately in the past. 5. Early Measurement by Roemer In the late 1600s, Claus Roemer studied the motion of Jupiter’s moons. • He noticed that the observed periods of the moons changed depending on Earth’s position. • He correctly concluded that light has a finite speed . • His calculated value was inaccurate, but his reasoning was correct. 6. Fizeau’s Experiment In 1849, Armand Fizeau became the first person to measure the speed of light on Earth.

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    Study Guide How the experiment worked: • Light passed through a gap in a rotating toothed wheel . • The light traveled to a mirror at distance d , reflected back, and passed through the wheel again. • The wheel’s speed was adjusted so the returning light passed through a neighboring gap. If: • the wheel rotates with angular speed ( \ omega ) • the angular separation between gaps is ( \ theta ) Then the time taken for light to travel a distance (2d) is: The speed of light is then calculated as: Modern laser techniques now measure the speed of light with accuracy to at least nine decimal places .

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    Study Guide 7. Polarization of Light Light can be polarized because it is a transverse wave . • In transverse waves, the oscillations occur perpendicular to the direction of motion. • Longitudinal waves , such as sound, cannot be polarized. What Is Polarized Light? • Unpolarized light vibrates in many different directions. • Polarized light vibrates in only one plane , perpendicular to the direction of travel. Unpolarized light from a bulb spreads out with vibrations in all directions. 8. Mechanical Analogy of Polarization Polarization can be explained using a mechanical example.

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    Study Guide • A wave travels through two slotted frames (polarizers). • If the slots are aligned, the wave passes through. • If the second frame is turned perpendicular , the wave is blocked and absorbed. 9. Polarization by Selective Absorption Some materials polarize light by absorbing certain vibration directions . • Tourmaline is a natural crystal that allows light to pass in only one polarization direction. • Such materials are called dichroic substances . Polaroid Filters • Polaroid is an artificial dichroic material. • It is made of long - chain hydrocarbons aligned in one direction. • These molecules absorb light whose electric field is parallel to the chains. • Light with an electric field perpendicular to the chains is transmitted.

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