Reflection of Light

Reflection is the phenomenon where a ray of light, upon striking a polished, smooth, or regular surface, bounces back into the same medium from which it originated.

Laws of Reflection

The reflection of light at any surface—whether plane or curved—is governed by two definitive physical laws:

• First Law: The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
• Second Law: The angle of incidence (i) is always equal to the angle of reflection (r). Mathematically, this is expressed as:
  i = r

Concept of Glancing Angle

The angle made by the incident ray or the reflected ray with the reflecting surface is known as the glancing angle (g). The relationship between the angle of incidence and the glancing angle is given by:

Angle of Deviation

The total angle by which a ray of light is deviated from its original path after one reflection is called the angle of deviation (δ). It is expressed as:

Types of Reflection

Based on the nature of the reflecting surface, reflection is classified into two distinct types:

Regular (Specular) Reflection

This occurs when a parallel beam of incident light falls on a smooth, highly polished surface (such as a plane mirror or still water) and reflects as a parallel beam in one definite direction. This type of reflection forms clear, sharp images.

Irregular (Diffuse) Reflection

This occurs when a parallel beam of incident light falls on a rough or uneven surface (such as wall, paper, or clothing) and reflects in various random directions.

• Key Fact: Diffuse reflection still obeys the laws of reflection at every microscopic point of contact. However, due to surface irregularities, the normals at different points are not parallel, causing the light to scatter. This type of reflection allows us to see non-luminous objects around us from any angle without glare.

Reflection from Plane Mirrors

A plane mirror is a thin, flat piece of glass silvered on one side to act as a highly reflective surface.

Characteristics of Images Formed by Plane Mirrors

• Virtual and Erect: The image cannot be projected onto a screen and stands upright.
• Size Equivalence: The size of the image is exactly equal to the size of the object.
• Distance Equivalence: The distance of the image behind the mirror is equal to the distance of the object in front of the mirror.
• Lateral Inversion: The left side of the object appears as the right side of the image, and vice versa (e.g., the reversed lettering on ambulances).

Crucial Plane Mirror Theorems for Prelims

• Minimum Height Rule: To see the full-length image of a person of height H, the minimum height of the plane mirror required is H/2.
• Mirror Rotation: If a plane mirror is rotated through an angle θ, keeping the incident ray fixed, the reflected ray rotates through an angle 2θ.
• Relative Velocity: If an object moves toward a stationary plane mirror with a velocity v, its image moves toward the mirror with a velocity v, and the relative velocity between the object and its image is $2v. </li> </ul> <h5>Number of Images Formed by Two Intersecting Plane Mirrors</h5> <p> When an object is placed between two plane mirrors inclined at an angle\theta, multiple images are formed due to successive reflections. The number of images (n) is calculated using the formula: <div class = "math-display">m = <span class = "math-frac"><span class = "math-frac-top">360°</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">θ</span></span></div> </p> <ul> <li> <b>Case 1:</b> Ifmis an <b>even integer</b>, the number of images is: <div class = "math-display">n = m – 1</div> (Regardless of whether the object is placed symmetrically or asymmetrically) </li> <li> <b>Case 2:</b> Ifmis an <b>odd integer</b> and the object lies <b>symmetrically</b> on the angle bisector: <div class = "math-display">n = m – 1</div> </li> <li> <b>Case 3:</b> Ifmis an <b>odd integer</b> and the object lies <b>asymmetrically</b>: <div class = "math-display">n = m</div> </li> <li> <b>Case 4:</b> If\theta = 0^\circ(parallel mirrors),m = \infty, resulting in an <b>infinite</b> number of images (e.g., inside a barber shop). </li> </ul> <h4>Reflection from Spherical Mirrors</h4> <p> Spherical mirrors are mirrors whose reflecting surfaces form a part of a hollow sphere. They are classified into two main categories: </p> <h5>Concave Mirror (Converging Mirror)</h5> <p> A spherical mirror whose reflecting surface is curved inward toward the center of the sphere. It converges a parallel beam of light falling on it. </p> <h5>Convex Mirror (Diverging Mirror)</h5> <p> A spherical mirror whose reflecting surface is curved outward away from the center of the sphere. It diverges a parallel beam of light falling on it. </p> <h4>Important Optical Terminology</h4> <ul> <li> <b>Pole (P):</b> The geometric center of the reflecting spherical surface. </li> <li> <b>Center of Curvature (C):</b> The center of the hollow sphere of which the mirror forms a part. </li> <li> <b>Radius of Curvature (R):</b> The radius of the sphere of which the mirror forms a part. </li> <li> <b>Principal Axis:</b> The straight line passing through the pole and the center of curvature of the mirror. </li> <li> <b>Principal Focus (F):</b> The point on the principal axis where light rays traveling parallel to the principal axis actually meet (concave) or appear to diverge from (convex) after reflection. </li> <li> <b>Focal Length (f):</b> The distance between the pole and the principal focus. For mirrors of small aperture, it is half the radius of curvature: <div class = "math-display">f = <span class = "math-frac"><span class = "math-frac-top">R</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">2</span></span></div> </li> </ul> <h4>Image Formation Summary for Spherical Mirrors</h4> <h5>Concave Mirror Image Matrix</h5> <p> The nature and position of the image formed by a concave mirror vary drastically based on the position of the object. </p> <table> <thead> <tr> <td><strong>Position of Object</strong></td> <td><strong>Position of Image</strong></td> <td><strong>Size of Image</strong></td> <td><strong>Nature of Image</strong></td> </tr> </thead> <tbody> <tr> <td>At Infinity</td> <td>At Focus (F)</td> <td>Highly Diminished (Point-sized)</td> <td>Real and Inverted</td> </tr> <tr> <td>Beyond Center of Curvature (C)</td> <td>BetweenFandC</td> <td>Diminished</td> <td>Real and Inverted</td> </tr> <tr> <td>At Center of Curvature (C)</td> <td>At Center of Curvature (C)</td> <td>Same Size</td> <td>Real and Inverted</td> </tr> <tr> <td>BetweenCandF</td> <td>BeyondC</td> <td>Magnified / Enlarged</td> <td>Real and Inverted</td> </tr> <tr> <td>At Focus (F)</td> <td>At Infinity</td> <td>Highly Magnified</td> <td>Real and Inverted</td> </tr> <tr> <td>Between Pole (P) and Focus (F)</td> <td>Behind the Mirror</td> <td>Magnified / Enlarged</td> <td><b>Virtual and Erect</b></td> </tr> </tbody> </table> <h5>Convex Mirror Image Matrix</h5> <p> A convex mirror <b>always</b> forms a virtual, erect, and diminished image, irrespective of the distance of the object from the mirror. </p> <table> <thead> <tr> <td><strong>Position of Object</strong></td> <td><strong>Position of Image</strong></td> <td><strong>Size of Image</strong></td> <td><strong>Nature of Image</strong></td> </tr> </thead> <tbody> <tr> <td>At Infinity</td> <td>At Focus (F) behind mirror</td> <td>Highly Diminished (Point-sized)</td> <td>Virtual and Erect</td> </tr> <tr> <td>Between Infinity and Pole (P)</td> <td>BetweenPandFbehind mirror</td> <td>Diminished</td> <td>Virtual and Erect</td> </tr> </tbody> </table> <h4>Real vs. Virtual Images</h4> <ul> <li> <b>Real Image:</b> Formed when light rays actually intersect at a point after reflection. It can be caught on a screen and is always inverted. </li> <li> <b>Virtual Image:</b> Formed when light rays do not actually meet but appear to diverge from a point when produced backward. It cannot be caught on a screen and is always erect. </li> </ul> <h4>Mathematical Formulation for Spherical Mirrors</h4> <h5>Mirror Formula</h5> <p> The relationship connecting the object distance (u), image distance (v), and focal length (f) is expressed as: <div class = "math-display"><span class = "math-frac"><span class = "math-frac-top">1</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">v</span></span> + <span class = "math-frac"><span class = "math-frac-top">1</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">u</span></span> = <span class = "math-frac"><span class = "math-frac-top">1</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">f</span></span></div> </p> <h5>Linear Magnification (m)</h5> <p> The ratio of the height of the image (h’) to the height of the object (h). It is also related touandv: <div class = "math-display">m = <span class = "math-frac"><span class = "math-frac-top">h’</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">h</span></span> = -<span class = "math-frac"><span class = "math-frac-top">v</span><span class = "math-frac-slash">/</span><span class = "math-frac-bottom">u</span></span></div> </p> <ul> <li> <b>Sign Convention Trivia:</b> Ifmis negative, the image is real and inverted. Ifmis positive, the image is virtual and erect. If|m| > 1, the image is magnified. </li> </ul> <h4>Practical Applications of Mirrors</h4> <h5>Applications of Concave Mirrors</h5> <ul> <li> <b>Shaving and Makeup Mirrors:</b> Used to see an enlarged, erect view of the face when placed close (betweenPandF). </li> <li> <b>Dentist Mirrors:</b> Used by dentists to see magnified images of teeth. </li> <li> <b>Headlights and Searchlights:</b> The light source is placed at the focus to produce a powerful, parallel beam of light that travels long distances. </li> <li> <b>Solar Furnaces:</b> Large concave mirrors focus sunlight at the principal focus to generate high temperatures for green energy production. </li> </ul> <h5>Applications of Convex Mirrors</h5> <ul> <li> <b>Rear-View Mirrors in Vehicles:</b> They provide an erect, though diminished, image and offer a much wider field of view compared to plane mirrors, enabling drivers to see a large area of traffic behind them. </li> <li> <b>Security Mirrors in Shops:</b> Installed in blind corners of supermarkets or parking lots to prevent theft and accidents. </li> </ul> <h5>Applications of Plane Mirrors</h5> <ul> <li> <b>Periscopes:</b> Used in submarines to view objects above the water surface, employing two parallel plane mirrors inclined at45^\circ. </li> <li> <b>Kaleidoscopes:</b> Used to create beautiful patterns using three plane mirrors inclined at60^\circ$ to each other.