Ray Model of Light Study Guide

Learning Outcomes

• Understanding the Ray Model: Demonstrate that the ray model represents the path taken by light.

• Plane Mirror Characteristics: Investigate the properties of images formed by a plane mirror.

• Laws of Reflection: Investigate that the angle of incidence ($\angle i$) is equal to the angle of reflection ($\angle r$), relative to the normal.

• Reflecting Surfaces: Describe the effects and applications of reflecting surfaces, including plane and curved (convex and concave) mirrors.

• Surface Texture and Reflection: Explain how reflection is affected by smooth versus rough surfaces using the ray model.

• Refraction and Speed of Light: Understand that changes in the speed of light in different media cause refraction (calculation of angles is not required).

• Effects of Refraction: Describe observable phenomena caused by refraction.

• Dispersion of Light: Describe how white light is dispersed by a prism using the ray model.

• Electromagnetic (EM) Radiation: Show awareness of the beneficial and harmful effects of EM radiation, specifically infrared, ultraviolet, and visible light.

• Technological Impact of Light: Understand the impact of light produced by technology on society and the environment, such as how city lights improve night visibility but cause light pollution, bird disorientation, and high electrical energy consumption.

Introduction to Light and Light Pollution

• Light as a Model: Scientists use scientific models to understand the world; the ray model is the tool used to understand the behavior of light.

• Importance of Light:

  • It is the only thing humans can actually see and is a primary form of energy.

  • Photosynthesis: Plants require light to synthesize food from air and minerals. Almost all living organisms depend on plants directly or indirectly for energy.

  • Temperature Regulation: Earth absorbs solar energy to maintain an inhabitable temperature.

• Light Pollution:

  • Definition: Unwanted or excessive artificial lighting resulting from urbanization.

  • Impact: Compromises human health and disrupts ecosystems.

  • Global Context: A 2016 Science Advances study named Singapore as the country with the worst level of light pollution in the world.

Fundamental Properties of Light

• Energy and Speed:

  • Light is a form of energy.

  • Speed in Vacuum: Light travels at a constant speed of $3.0 \times 10^8\,m/s$.

  • Comparison to Sound: Light travels much faster than sound, which has a speed of approximately $330\,m/s$ in air.

• Visibility: An object is seen only when light from that object enters the eyes.

• Interactions with Matter: When light hits an object, it can be:

  • Reflected: Bounces off the surface.

  • Refracted: Bends as it passes through.

  • Absorbed: Taken in by the object.

• Transparency and Opacity:

  • The more transparent an object is, the less light it absorbs.

  • Opaque objects reflect or absorb light.

• Path of Light:

  • Light rays travel in straight lines if moving within the same medium.

  • Principle of Reversibility: Light rays retrace the same path if they are reversed. This explains why if you can see someone in a mirror, that person can also see you.

Ray Diagrams and Drawing Rules

• Definition: A ray diagram shows how light travels and what happens when it reaches a surface. In the ray model, light is represented as straight lines with arrows (rays) showing the direction from the source.

• Drawing Rules:

  1. Light rays must be drawn as straight lines using a ruler and a sharp pencil.

  2. Real Light Rays: Drawn as solid lines.

  3. Virtual (Imaginary) Light Rays: Drawn as dotted lines.

  4. Arrows: All real light rays must include arrows to show the direction of travel. Virtual rays do not require arrows.

• Symbolic Representation: In diagrams, a plane mirror is represented by a straight line with shading (hachures) on the non-reflecting side.

Reflection of Light

• General Concept: All surfaces reflect light to some extent. Reflection involves light rays "bouncing off" a surface.

• The Two Laws of Reflection:

  1. The angle of incidence ($\angle i$) is equal to the angle of reflection ($\angle r$).

  2. The incident ray, the reflected ray, and the normal at the point of incidence all lie on the same plane.

• Terminologies:

  • Incident Ray: The light ray approaching the surface.

  • Point of Incidence: The exact point where the incident ray meets the surface.

  • Reflected Ray: The light ray bouncing off the surface.

  • Normal: An imaginary line perpendicular ($90^o$) to the reflecting surface, passing through the point of incidence.

  • Angle of Incidence ($\angle i$): The angle between the incident ray and the normal.

  • Angle of Reflection ($\angle r$): The angle between the reflected ray and the normal.

  • Critical Note: Angles are always measured from the normal, never from the reflecting surface itself.

• Types of Reflection:

  • Regular Reflection: Occurs on smooth surfaces (e.g., mirrors). A parallel beam of incident light remains parallel after reflection, allowing for clear images.

  • Diffused Reflection: Occurs on rough or uneven surfaces. Parallel incident rays are reflected in many different directions, preventing clear image formation.

Characteristics of Images Formed by Plane Mirrors

• Real vs. Virtual Images:

  • Real Image: Light actually falls where the image is located; it can be caught on a screen (e.g., a projector image).

  • Virtual Image: No light rays pass through the image location; it cannot be caught on a screen (e.g., mirror images, spectacles for shortsightedness).

• Plane Mirror Properties:

  1. Upright: The orientation is the same as the object.

  2. Size: The image is the same size as the object.

  3. Distance: The image appears as far behind the mirror as the object is in front of it.

  4. Virtual: It cannot be projected on a screen.

  5. Laterally Inverted: Right becomes left and left becomes right.

Steps for Constructing a Ray Diagram for a Plane Mirror

1. Locate the Image:

   • Draw a dotted line from the object (O) perpendicular to the mirror surface (MN) and extend it behind the mirror.

   • Measure the distance from O to the mirror. Mark the image (I) at the same distance behind the mirror on the perpendicular line.

2. Draw Paths to the Eye:

   • Join image (I) to the observer's eye (E).

   • Use a dotted line behind the mirror (indicating virtual rays).

   • Use a solid line in front of the mirror (indicating real reflected rays). Add direction arrows to the solid lines.

3. Complete the Ray from the Object:

   • Join object (O) to the point of incidence where the line from (I) meets the mirror (MN). If drawn correctly, $\angle i$ will equal $\angle r$.

Uses of Reflecting Surfaces

• Plane Mirrors:

  • Checking personal appearance.

  • Interior design: Placed on walls to make rooms appear wider.

  • Optical instruments: Used in periscopes to see over obstacles or around corners. In a periscope, the final image is not laterally inverted.

• Curved Mirrors:

  1. Convex Mirrors (Curves outward):

     • Image Properties: Virtual, upright, and diminished (smaller than the object).

     • Application: Provides a wide field of vision. Used as security mirrors in shops, rear-view/side mirrors in cars, staircase mirrors on double-decker buses, and blind corner mirrors on roads.

  2. Concave Mirrors (Curves inward):

     • Image Properties: Virtual, upright, and magnified (larger than the object).

     • Application: Used for magnification, such as cosmetic mirrors and dental mirrors.

     • Light Projection: Used in car headlights and searchlights to reflect light from a bulb into a strong, focused beam.

     • Microscopy: Found at the base of microscopes to reflect light toward a specimen.

Refraction

• Definition: Refraction is the bending of light (change in direction) as it passes from one transparent medium to another due to a change in the speed of light.

• Direction of Bending (Mnemonic: FAST):

  • Faster (entering less dense medium) -> bends Away from the normal.

  • Slower (entering denser medium) -> bends Towards the normal.

• Optical Density:

  • Tells us how fast or slow light travels in a medium. It is distinct from mass density.

  • Rule: Higher optical density = slower speed of light = more bending towards the normal.

  • Comparison: Air has a lower optical density than glass or water.

• Boundary Constraints:

  • Refraction occurs only at the boundary (interface) between two media.

  • Within a single medium, light travels in a straight line.

  • Zero Angle of Incidence: If a light ray hits the surface at $90^o$ ($\angle i = 0^o$), there is no bending/change in direction. However, the speed of light still increases or decreases.

Phenomena and Effects of Refraction

• Optical Illusions:

  • Objects under water appear at a different depth than they actually are because light bends when moving from water into air.

  • A spoon in a glass of water may appear broken, or a stick may appear shallower and bent.

• Apparent Depth:

  • A man looking at a scuba diver sees the diver at a shallower depth.

  • A scuba diver looking at a man on the surface sees the man further away from the water surface.

• Drawing Apparent Position (Coin in bucket):

  1. Draw the virtual image (I) directly above the object (O) using dotted lines.

  2. Draw two straight solid lines from the water surface to the eye (direction arrows needed).

  3. Draw dotted lines from the image (I) to the same points on the water surface.

  4. Trace real rays from the object (O) to those same surface points.

Dispersion of Light

• Visible Light Composition: White light is a spectrum of colors: Red, Orange, Yellow, Green, Blue, Indigo, and Violet (ROYGBIV).

• Dispersion: The separation of white light into its component colors using a prism.

• Mechanism: Each color of white light travels at a slightly different speed through the glass prism and thus refracts at a different angle.

  • Red: Bends the least; slows down the least.

  • Violet: Bends the most; slows down the most.

• Recombination: Colors can be turned back into white light using a second, inverted prism.

Impact of Electromagnetic (EM) Radiation