Properties of Waves - Reflection

• In Physics 20, the behavior of waves upon striking barriers was explored, leading to key conclusions regarding their properties during reflection.   - 1.) Waves that strike a barrier reflect at an angle equal to the angle they strike the barrier.   - 2.) During reflection, waves retain their speed, frequency, and wavelength properties.

• Visible light and all electromagnetic radiation (EMR) exhibit similar wave behavior when they strike reflective surfaces.

The Law of Reflection

• Reflection is a straightforward concept, often misunderstood by some. All electromagnetic radiation reflects off appropriate surfaces.

When to Use Caution

• Care must be taken in circumstances involving irregular surfaces.

Focus on Visible Light

• The current discussion focuses solely on visible light reflecting off mirrors. Diagrams of reflection should always include:   - A normal line drawn perpendicularly to the reflective surface at the point of incidence.

Angle of Incidence and Reflection

• The Law of Reflection states:   - "The angle of incidence equals the angle of reflection."   - Both angles are measured from the normal line, ensuring a common reference point.   - Example of regular reflection is shown in how light behaves on a smooth surface.   - Irregular (diffuse) reflection can occur, such as on a windy lake, resulting in a blurred image due to light reflecting in multiple directions.

Plane Mirror Diagrams

• Using the Law of Reflection, one can predict how an observer perceives an image in a plane mirror.
• Key principles for plane mirrors:   - 1. The image size equals the size of the original object.   - 2. The distance from the image to the mirror equals the distance from the object to the mirror.   - 3. Light behaves according to the Law of Reflection, bouncing off the mirror at the same angle it hit.

Illustrating Light Rays

• Diagrams illustrate how light rays travel from an object to the observer's eye, explaining why the image appears behind the mirror.   - The image is referred to as a "virtual image" since there are no real light rays behind the mirror, indicated by dotted lines in diagrams.   - A mental test can confirm a virtual image: if placing paper where the image appears does not show the image, it is likely a virtual image.

Curved Mirrors

• In contrast to plane mirrors, curved mirrors (like those in funhouses) change perception dramatically:   - Typically, we will analyze concave (converging) and convex (diverging) mirrors.

Concave Converging Mirrors

• Imagine a section cut from a giant metal ball with a shiny interior:   - Key components of concave mirrors include:     - Centre (C): Center of the sphere.     - Focal Point (F): Point where light converges when the object is infinitely far away. It is halfway between the mirror surface and the center, representing the focal length.     - Principal Axis (PA): A reference line passing through the center perpendicular to the mirror surface.     - Vertex (V): Intersection of the principal axis and the mirror surface.

Rules for Image Formation in Concave Mirrors

• When determining the image position created by a concave mirror, follow three rules (only two are needed to locate the image):   - Rule #1: A ray through the focal point reflects parallel to the principal axis.   - Rule #2: A ray parallel to the principal axis reflects through the focal point.   - Rule #3: A ray passing through the center reflects back through the center, though this method is less reliable.

Classifying Images

• Images from concave mirrors must be classified:   - Description: Size and nature.   - Magnification: Same / Enlarged / Diminished.   - Attitude: Erect / Inverted.   - Type: Real / Virtual.

Convex Diverging Mirrors

• Convex mirrors follow similar rules but result in a different appearance:   - The focal point and center are positioned behind the mirror.   - They typically create diminished virtual images of the original object, as reflected rays diverge.

Mirror Equations

• To locate the position and characteristics of images in mirrors, utilize:   - Mirror Equation:
  $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$
      where:     - $f$: focal length (m)     - $d_o$: distance from the mirror to the object (m)     - $d_i$: distance from the mirror to the image (m)     - An object must always be positioned in front of the mirror to project an image.

• Magnification Equation:
  $m = \frac{h_i}{h_o} = \frac{d_i}{d_o}$
      where:     - $h_i$: height of the image (m)     - $h_o$: height of the object (m)     - $m$: magnification factor (size comparison).

Special Notes on Signs

• Using the Mirror Equation:   - Real Objects (in front of mirror) → Positive   - Virtual Objects (behind mirror) → Negative   - Focal lengths follow similar rules:     - Converging mirrors have positive focal lengths.     - Diverging mirrors have negative focal lengths.

• Using the Magnification Equation:   - Same sign conventions apply:     - Above the Principal Axis → Positive     - Below the Principal Axis → Negative     - Magnification Quantities:       - $m < 1$: Diminished       - $m = 1$: Same       - $m > 1$: Enlarged.

Examples

• Example 3: A diverging mirror with a radius of 20 cm has an object placed 30 cm in front of it. Determine the image position.
• Example 4: For the situation in Example 3, find the image height given an initial height of the object at 5.0 cm and calculate the magnification.