Hello, and welcome to today's physics lesson. Today, we begin Chapter Seven: Reflection of Light. Over the next several minutes, we will explore how light bounces off surfaces, understand the laws that govern this behaviour, and discover how mirrors—both flat and curved—create the images we see. By the end, you will understand plane mirrors, spherical mirrors, and how to predict where images form.
Let us start with the basics. When light strikes a surface, part of it returns into the same medium. This phenomenon is called reflection. The light that returns is reflected light, while the rest may be absorbed or transmitted depending on the surface. It is reflection that allows us to see the world around us. Luminous objects like the sun emit their own light, but non-luminous objects—like this page or your desk—are visible only because they reflect light into your eyes.
Surfaces vary in how they reflect light. A highly polished, silvered surface like a plane mirror reflects almost all incident light. A plane mirror is made from a glass plate, with one surface polished smooth and the other coated with silver or mercury, then protected with an opaque backing. Light enters through the polished front and reflects strongly from the silvered back.
There are two kinds of reflection. Regular reflection occurs when parallel light rays hit a smooth surface like a mirror. The reflected rays remain parallel and travel in a fixed direction. You see a bright, clear reflection only from specific angles. Irregular or diffused reflection happens when light strikes a rough surface like a wall or paper. Although each ray obeys the laws of reflection, the uneven surface sends rays in many directions. This diffused light is why we can see objects from anywhere in a room.
Before we state the laws of reflection, let us define some essential terms. The incident ray is the light ray striking the surface. The point where it strikes is the point of incidence. The reflected ray is the ray that bounces back into the same medium. The normal is a line perpendicular to the surface at the point of incidence. The angle of incidence, denoted by i, is the angle between the incident ray and the normal. The angle of reflection, denoted by r, is the angle between the reflected ray and the normal.
Now, the laws of reflection. These are precise and universal. First: the angle of incidence equals the angle of reflection. Second: the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. These laws hold true for every reflecting surface, whether plane or curved.
A special case: when light strikes a mirror normally—that is, perpendicular to the surface—the angle of incidence is zero degrees. Therefore, the angle of reflection is also zero, and the ray retraces its path straight back.
How do we verify these laws experimentally? Fix a sheet of white paper on a board and draw a line representing the mirror's position. Mark a point and draw a normal. Place a plane mirror vertically along the line. Fix two pins in a straight line at an angle to the mirror. View their images from the other side of the normal, and place two more pins so they appear aligned with the images of the first pair. Remove the mirror and pins, then join the points. You will find the angles of incidence and reflection are equal, confirming the first law. Since all pins lie on the flat paper, the rays and normal share the same plane, confirming the second law.
Let us now understand how images form. From every point on an illuminated object, light travels in all directions. To locate an image, we trace at least two rays from a point on the object after they reflect. Where these reflected rays actually meet, or appear to meet when extended backward, is the image point.
Images are classified as real or virtual. A real image forms where reflected rays actually converge. It can be projected on a screen and is always inverted. A virtual image forms where rays only appear to diverge from; they meet only when extended backward. It cannot be projected and is always erect.
For a plane mirror, consider a point object in front. Two rays strike the mirror, reflect according to the laws, and enter your eye. Your brain traces these rays backward, and they appear to originate from a point behind the mirror. This is the virtual image. For an extended object, each point has a corresponding image point behind the mirror.
The image formed by a plane mirror has these characteristics: it is erect, virtual, the same size as the object, and laterally inverted. Lateral inversion means left and right are swapped. Your left hand appears as a right hand in the mirror. This is why the word AMBULANCE is written in reverse on emergency vehicles—drivers see it correctly in their rear-view mirrors.
The image distance equals the object distance. If you stand two metres from a mirror, your image appears two metres behind it, making you four metres from your image.
2d
Similarly, if you move toward the mirror with speed v, your image appears to move toward you with speed 2v.
Now consider what happens with two mirrors. When mirrors are parallel, an object between them produces infinite images. Each image in one mirror acts as an object for the other, creating a series that fades into the distance. Barber shops use this arrangement so you can see the back of your head.
When two mirrors are perpendicular—at ninety degrees to each other—three images form. The formula for the number of images depends on the angle θ between mirrors. Calculate n = 360°/θ, where θ is in degrees. If n is even, the number of images is always n − 1, regardless of where the object is placed. If n is odd, the number of images is n when the object is placed asymmetrically, and n − 1 when placed symmetrically on the angle bisector.
Geometrically, the object and all images lie on a circle centered at the mirrors' intersection, with radius equal to the object's distance from that point.
We now turn to spherical mirrors—reflecting surfaces that are parts of hollow spheres. There are two types. A concave mirror is silvered on the outer, bulging surface, so reflection occurs from the inner, hollow surface. It converges light rays. A convex mirror is silvered on the inner surface, so reflection occurs from the outer, bulging surface. It diverges light rays.
Several terms describe spherical mirrors. The centre of curvature is the centre of the sphere from which the mirror was cut. The radius of curvature, R, is the distance from this centre to any point on the mirror. The pole is the geometric centre of the mirror's surface. The principal axis is the straight line joining the pole to the centre of curvature.
The focus is crucial. For a concave mirror, rays parallel to the principal axis reflect and converge at the focus. This is a real focus, located in front of the mirror. For a convex mirror, parallel rays reflect and appear to diverge from a focus behind the mirror. This is a virtual focus. The focal length, f, is the distance from pole to focus.
Here is a fundamental relationship: the focal length equals half the radius of curvature. In symbols, f = R/2. Or equivalently, R = 2f. This holds for both concave and convex mirrors. For example, a concave mirror with radius of curvature 20 cm has focal length 10 cm.
To construct ray diagrams, we use special rays. First, a ray through the centre of curvature strikes normally and retraces its path. Second, a ray parallel to the principal axis reflects through—or appears to come from—the focus. Third, a ray through the focus reflects parallel to the principal axis. Fourth, a ray striking the pole reflects with equal angles to the principal axis.
Let us trace images in a concave mirror as the object moves. With the object at infinity, the image forms at the focus: real, inverted, and reduced to a point. As the object moves closer but remains beyond the centre of curvature, the image lies between the focus and centre of curvature: real, inverted, and diminished. At the centre of curvature, the image is also at the centre of curvature: real, inverted, and the same size.
Between the centre of curvature and focus, the image moves beyond the centre of curvature: real, inverted, and magnified. At the focus, the image forms at infinity. Between the focus and pole, the image forms behind the mirror: virtual, upright, and magnified. This is why concave mirrors work as shaving mirrors—your face, placed inside the focal length, appears enlarged and upright.
For convex mirrors, the situation is simpler. Regardless of object position, the image always forms between the pole and focus behind the mirror. It is always virtual, upright, and diminished. As the object approaches from infinity, the image moves from the focus toward the pole, growing slightly larger but remaining smaller than the object.
We use sign conventions to handle calculations. All distances are measured from the pole. Distances along the incident light direction are positive; opposite are negative. Distances above the principal axis are positive; below are negative. For concave mirrors, focal length is negative; for convex mirrors, it is positive.
The mirror formula relates object distance u, image distance v, and focal length f. One over f equals one over u plus one over v. In symbols, 1/f = 1/u + 1/v. This formula applies to both concave and convex mirrors when proper sign conventions are followed. Always substitute values with proper signs. For concave mirrors, u and f are negative; v is negative for real images, positive for virtual. For convex mirrors, u is negative while v and f are positive.
Linear magnification m equals the ratio of image height to object height, which equals minus v/u. In symbols, m = −v/u. Negative magnification indicates a real, inverted image. Positive magnification indicates a virtual, erect image.
Finally, the practical uses of spherical mirrors. Concave mirrors serve as shaving mirrors when your face lies between pole and focus. They are reflectors in torches and vehicle headlights, with the light source at the focus to produce parallel beams. Doctors use them as head mirrors to concentrate light onto small body areas.
Convex mirrors spread light over larger areas in street lamps. Most importantly, they serve as rear-view mirrors in vehicles. They provide a wider field of view than plane mirrors of the same size, though the image is diminished. This wider view helps drivers see more traffic behind them.
To distinguish mirrors without touching: hold each near your face. If the image is same-sized and unmoving when you move the mirror toward or away from your face, it is a plane mirror. If upright and magnified, with the magnification decreasing as you pull away, it is a concave mirror. If upright and diminished, growing smaller as you pull away, it is a convex mirror.
Let us recap the essential points. First, reflection follows two laws: angle of incidence equals angle of reflection, and all rays lie in one plane. Second, plane mirrors produce virtual, erect, same-sized images with lateral inversion. Third, multiple mirrors create multiple images depending on their angle. Fourth, spherical mirrors have focal length equal to half the radius of curvature. Fifth, concave mirrors can produce real or virtual images depending on object position; convex mirrors always produce virtual, erect, diminished images. Sixth, the mirror formula and magnification formula govern quantitative problems. The mirror formula is one over f equals one over u plus one over v. In symbols, 1/f = 1/u + 1/v. Magnification is m equals minus v/u. In symbols, m = −v/u.
That concludes our lesson on Reflection of Light. You now understand how light behaves at surfaces, how images form in mirrors, and how to predict their positions and nature. Practice drawing ray diagrams and applying the mirror formula to build confidence. Keep curious, keep observing the optics around you, and I look forward to our next physics lesson together.