Light Reflection

Definition: Reflection occurs when light bounces off a surface. When light traveling through one medium encounters a boundary with another medium, part of it bounces back into the original medium. This phenomenon allows us to see objects that don't produce their own light - light from sources like the Sun or lamps reflects off surfaces and into our eyes. Reflection occurs on all surfaces, but the quality depends on surface smoothness. Understanding reflection is fundamental to optics, from mirrors to fiber optics to the design of solar panels.

Mathematical Derivation - Fermat's Principle:

The law of reflection can be derived from Fermat's principle of least time. Light traveling from point A to point B takes the path that minimizes travel time. Consider reflection from a plane:

The Laws of Reflection:

1. First Law: The angle of incidence equals the angle of reflection (∠i = ∠r), where angles are measured from the normal
2. Second Law: The incident ray, reflected ray, and normal all lie in the same plane (the plane of incidence)

Worked Example 1: A light ray strikes a mirror at 35° to the surface. What is the angle of reflection?

Worked Example 2: Two mirrors are placed at 90° to each other. A ray hits one mirror at 30° incidence. Find the final direction of the reflected ray.

Worked Example 3: Calculate the deviation angle for a ray reflecting from a plane mirror.

Key Terms:

• Normal: Imaginary line perpendicular (90°) to reflecting surface at the point of incidence
• Angle of Incidence (i): Angle between incident ray and normal
• Angle of Reflection (r): Angle between reflected ray and normal
• Incident Ray: Incoming light ray approaching the surface
• Reflected Ray: Light ray bouncing off the surface
• Angle of Deviation: D = 180° - (i + r) = 180° - 2i for plane mirrors

Types of Reflection:

• Regular (Specular) Reflection: Occurs on smooth, polished surfaces like mirrors. All reflected rays travel in the same direction, producing clear images. The surface irregularities are smaller than the light wavelength.
• Diffuse Reflection: Occurs on rough surfaces. Light scatters in many directions because each microscopic surface section has a different orientation. This enables us to see non-luminous objects from any angle.
• Mixed Reflection: Some surfaces exhibit both regular and diffuse components, like brushed metal or semi-gloss paint.

Plane Mirror Image Characteristics:

• Image distance = Object distance from mirror (behind the mirror by same amount)
• Virtual image: Cannot be projected on a screen (formed behind the mirror)
• Lateral inversion: Left and right appear swapped (actually front-back reversal)
• Same size as object: Magnification m = -1 (negative indicates virtual image)
• Upright orientation: Image is not inverted top-to-bottom
• Field of view: A mirror shows everything visible within a certain angular range

Mirror Formula and Magnification:

Where: f = focal length, u = object distance, v = image distance, R = radius of curvature, m = magnification, h = object height, h' = image height

Sign Convention (New Cartesian Sign Convention):

• All distances measured from the pole (vertex) of the mirror
• Object distance (u): Always negative (object is in front of mirror)
• Real image distance: Positive (formed in front of mirror)
• Virtual image distance: Negative (formed behind mirror)
• Heights above principal axis: Positive
• Focal length: Positive for concave mirrors, negative for convex mirrors

Spherical Mirrors:

• Concave Mirror: Inner (curved inward) surface reflects. Used in flashlights, headlights, makeup mirrors, dental mirrors, and solar concentrators. Can form real or virtual images depending on object position.
• Convex Mirror: Outer (curved outward) surface reflects. Used as security and surveillance mirrors, vehicle side mirrors ( passenger side), and shop anti-theft mirrors. Always forms virtual, diminished (smaller) images with wider field of view.

Image Formation by Spherical Mirrors:

Concave Mirrors:

• Object beyond center C: Real, inverted, smaller ( diminished ) image
• Object at center C: Real, inverted, same size image
• Object between C and F: Real, inverted, magnified (larger) image
• Object at focal point F: Image at infinity (parallel reflected rays)
• Object between F and mirror: Virtual, upright, magnified image (used in vanity mirrors)

Convex Mirrors:

• Object anywhere in front: Virtual, upright, diminished image
• As object approaches infinity, image approaches focal point

Real-World Applications:

• Everyday Mirrors: Personal grooming (bathroom mirrors, makeup mirrors), vehicle rearview mirrors (driver's side is plane, passenger side is often convex for wider view)
• Reflecting Telescopes: Newtonian telescopes use concave primary mirrors; Cassegrain telescopes use both concave primary and convex secondary mirrors. These are superior to refracting telescopes for large apertures.
• Periscopes: Used in submarines, trench warfare, and seeing over obstacles. Two plane mirrors at 45° redirect light水平ly. Prism periscopes use total internal reflection for greater durability.
• Solar Concentrators: Parabolic trough mirrors focus sunlight onto receivers, heating fluid to generate electricity. Used in concentrated solar power (CSP) plants.
• Road Safety and Retroreflection: Cat's eyes, road signs, and bike reflectors use retroreflectors that bounce light back toward its source using corner reflectors (90° angles). This makes them highly visible to drivers.
• Kaleidoscopes and Sextants: Kaleidoscopes use multiple mirrors at fixed angles to create symmetrical patterns. Sextants use a movable mirror to measure angles between celestial objects and horizon for navigation.
• Laser Cavities: Lasers use highly reflective mirrors to create optical feedback. The gain medium sits between mirrors, and light bounces thousands of times, amplifying through stimulated emission.
• Automotive Headlights: Parabolic mirrors behind bulbs reflect and focus light into a beam. Complex reflector shapes distribute light appropriately for high/low beams.

Why is the Sky Blue? Rayleigh scattering: atmospheric molecules scatter shorter wavelengths (blue, violet) much more efficiently than longer wavelengths (red, yellow). Blue light (λ ≈ 450 nm) scatters about 10 times more than red light (λ ≈ 650 nm). We see blue from all directions because scattered blue light reaches our eyes. Violet is also scattered heavily, but our eyes are less sensitive to it, and some violet is absorbed by the upper atmosphere.

Advanced Topic - Retroreflection: Some surfaces reflect light back toward its source regardless of incident angle. Corner reflectors (three mutually perpendicular mirrors) use two reflections to achieve this. The Moon's surface acts as a rough retroreflector; Apollo astronauts left retroreflectors used for precise Earth-Moon distance measurements (accurate to millimeters).

Common Mistakes to Avoid:

• Measuring from Surface: Angles must be measured FROM THE NORMAL, not from the mirror surface. A ray "at 30° to the mirror" is actually at 60° incidence.
• Confusing Lateral Inversion: Mirrors flip front-back, not left-right. When you raise your right hand, your image raises the hand on the opposite side (left side of image), which is actually your right hand facing the mirror.
• Thinking Virtual Images are Not Real: Virtual images are still real in the sense that your brain interprets them as existing. They're just not projectable onto a screen because light doesn't actually pass through the image location.
• Ignoring Sign Conventions: In mirror formulas, signs matter. Positive and negative distinguish real/virtual images and magnification direction. Always use the agreed-upon sign convention consistently.
• Applying Plane Mirror Formula to Curved Mirrors: The simple "image distance = object distance" only applies to plane mirrors. Spherical mirrors follow the mirror formula and have different image properties.
• Assuming All Reflection is Specular: Most surfaces are rough at the microscopic level. What appears smooth to the eye still produces some diffuse reflection, which is why we can see surfaces from angles.
• Confusing Focal Point and Center of Curvature: Focal point is halfway between mirror and center of curvature. Light through the center of curvature reflects back on itself; light through the focal point reflects parallel.