Physics Study Guide: Reflection of Light and Plane Mirrors

Characteristics of Images in Plane Mirrors (KPI 22.2)

Size and Orientation: * The image formed in a plane mirror is exactly the same size as the object being reflected ( $\text{Size}_{\text{image}} = \text{Size}_{\text{object}}$ ). * The image is described as being "the right way up" (upright). * It is not inverted (upside down), but it is laterally inverted.
Lateral Inversion: * This is the phenomenon where the left and right sides of the object are swapped in the image. * If a person writes the word "LEFT" on a card and looks at it in a plane mirror, they will see the letters and the word flipped horizontally. * If a student looks at the letter "P" on paper, the reflection in the mirror will appear as the mirror-image of "P" (resembling a lower-case "q").
Nature of the Image: * Images in plane mirrors are always virtual. A virtual image is one where light rays appear to come from a point behind the mirror but do not actually pass through that point; such images cannot be captured on a screen.
Position and Distance: * The image is formed behind the mirror at the same distance the object is in front of the mirror. * If an object is placed $5\,cm$ in front of a mirror, the image is formed $5\,cm$ behind the mirror. The total distance between the object and the image is $10\,cm$ .
Reflection of Gauges and Clocks: * When viewing a clock in a plane mirror, the positions of the hands are laterally inverted. For example, if a reflected image looks like 04:15, the actual time is typically 07:45.
Relative Motion of Images: * If a person stands $1.0\,m$ in front of a mirror and the mirror moves away from the person at a speed of $1.0\,m/s$ , the distance between the person and the mirror increases by $1.0\,m$ every second. * Because the image stays same distance behind the mirror as the object is in front, the image also moves $1.0\,m/s$ away from the mirror. * Consequently, the image moves away from the person at a total speed of $2.0\,m/s$ (the sum of the mirror's speed relative to the person and the image's speed relative to the mirror).

The Law of Reflection and Geometric Terminologies (KPI 22.1 & 22.3)

Key Geometric Lines and Points: * Normal: A dashed line drawn at a right angle ( $90^\circ$ ) to the surface of the mirror at the point of incidence (labeled as line $X$ in many diagrams). * Incident Ray: The ray of light traveling toward the mirror. * Reflected Ray: The ray of light that bounces off the mirror surface.
Angles of Reflection: * Angle of Incidence ( $i$ ): The angle between the incident ray and the normal. * Angle of Reflection ( $r$ ): The angle between the reflected ray and the normal.
The Law of Reflection: * The fundamental rule is: The angle of incidence is always equal to the angle of reflection ( $i = r$ ). * Example: If light is incident on a mirror at an angle of $38^\circ$ , the angle of reflection is exactly $38^\circ$ . * Example: If the angle between the incident ray and the mirror surface itself is $35^\circ$ , one must first calculate the angle of incidence: $90^\circ - 35^\circ = 55^\circ$ . Therefore, the angle of reflection is also $55^\circ$ .
Consistency Across Surfaces: * Even if the angle of incidence is changed (e.g., from $45^\circ$ to $20^\circ$ ), the law $i = r$ holds true, so the new angle of reflection would be $20^\circ$ .

Analysis of Image Formation and Ray Diagrams (KPI 22.1, 22.4)

Ray Diagram Construction: * To correctly mark the position of an image ( $I$ ) for an object ( $O$ ), the image must be placed directly opposite the object across the mirror line at an equal distance. * A ray diagram is considered incorrect if the image position is not equidistant from the mirror according to the scale or if the law of reflection is not followed at the point of incidence.
Parallel Mirrors: * When light is reflected by two parallel plane mirrors (labeled X and Y), the geometry remains consistent. If light hits mirror X at a certain angle of incidence, it will hit mirror Y at a predictable angle based on alternate interior angles and the normals.
Light Beams and Obstructed Paths: * A parallel beam of light incident on a plane mirror will reflect as a parallel beam. The rays do not converge or diverge upon reflection from a flat surface. * When light strikes a mirror at an angle of $45^\circ$ to the surface, and the incident ray is initially parallel to a table, the reflected ray will be perprendicular to that initial path (making a $90^\circ$ angle with the original direction, or $45^\circ$ relative to the mirror surface).
Mirror Rotation: * If a mirror is rotated while the incident ray remains unchanged, the angle of incidence changes. * Specifically, if a mirror rotates through an angle of $10^\circ$ , the reflected ray rotates through an angle of $20^\circ$ ( $2 \times \theta$ ).

Complex Scenarios and Real-World Applications

Multiple Reflections in Glass: * When looking from a brightly-lit room into a thick glass window when it is dark outside, two images of one's face might be visible. This occurs because reflection happens at both the front surface of the glass and the back surface of the glass.
Building-to-Building Reflection (Police Helicopter Scenario): * In a scenario where a light beam from a helicopter hits a window ( $H$ ) on one apartment block across a road from another: * The normal is drawn perpendicular to the window surface at the point of incidence. * The angle of incidence is the angle between the incoming helicopter beam and that normal. * Following the law of reflection ( $i = r$ ), the beam will bounce off window $H$ and hit a corresponding window on the opposite building. To determine which window is hit, one must trace the reflected ray to the other side of the road.
Height and Distance Calculations: * If an object has a height of $2\,cm$ , its image will also have a height of $2\,cm$ . * If an object is $5\,cm$ from the mirror, and the image is $5\,cm$ behind it, the total distance separating the object and the image is $10\,cm$ .

Free Response and Diagram Tasks

Identifying Components: * Point of Incidence: The exact spot where the ray hits the mirror. * Dashed line at right angles: The Normal. * Labeling angles: The angle between the incoming ray and normal is $i$ ; the angle between the outgoing ray and normal is $r$ .
Types of Images (Real vs. Virtual): * Any image formed by a single plane mirror is virtual. * "Real" refers to images that can be projected (like those in a camera or on a movie screen); plane mirrors do not produce these.
Drawing Exercises: * When drawing the secondary path for multiple rays ( $X$ and $Y$ ) from one object ( $O$ ), each ray must follow the law of reflection individually at their respective points of contact with the mirror. * Both reflected rays, if traced backward behind the mirror, should intersect at the exact point where the virtual image ( $I$ ) is located.