Comprehensive theory, key formulas, diagrams, and memory aids for Light – Reflection and Refraction.
We see the world around us because of light. Light is a form of electromagnetic energy that causes the sensation of vision. While light exhibits properties of both waves and particles, in this chapter, we will treat light as traveling in straight lines (rectilinear propagation), exploring how it interacts with surfaces through reflection and refraction.
When light falls on a highly polished surface, like a mirror, most of the light is sent back into the same medium. This phenomenon is called the reflection of light.
These laws apply to all types of reflecting surfaces, including spherical surfaces.
Mirrors whose reflecting surfaces are spherical are called spherical mirrors. They can be thought of as a part of a hollow sphere of glass. 1. Concave Mirror: The reflecting surface is curved inwards (towards the center of the sphere). Think of looking into the "cave" of the spoon. 2. Convex Mirror: The reflecting surface is curved outwards. Think of the back of a spoon.
We use ray diagrams to locate images formed by mirrors. The intersection of at least two reflected rays gives the position of the image.
We use the New Cartesian Sign Convention: * The pole (P) is taken as the origin (0,0). * The principal axis is taken as the x-axis. * Object is always placed to the left of the mirror. * Distances measured to the right of the origin are positive (+), and to the left are negative (-). * Distances measured perpendicular to and above the principal axis are positive (+), and below are negative (-).
Mirror Formula: $$ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} $$ Where: * $v$ = image distance * $u$ = object distance * $f$ = focal length
Magnification (m): It gives the relative extent to which the image is magnified with respect to the object size. $$ m = \frac{Height\ of\ image\ (h')}{Height\ of\ object\ (h)} = -\frac{v}{u} $$ (Note: A negative 'm' indicates a real image; a positive 'm' indicates a virtual image).
Have you noticed that a pencil partially immersed in water appears bent at the surface? This happens because light travels at different speeds in different media. Refraction is the bending of light when it passes obliquely from one transparent medium to another.
The refractive index links to the relative speed of light in different media. $$ \text{Refractive index of medium 2 w.r.t medium 1 } (n_{21}) = \frac{\text{Speed of light in medium 1 } (v_1)}{\text{Speed of light in medium 2 } (v_2)} $$ Absolute Refractive Index: If medium 1 is vacuum or air, the refractive index of medium 2 is considered with respect to vacuum. $$ n_m = \frac{\text{Speed of light in vacuum } (c)}{\text{Speed of light in the medium } (v)} $$ (Note: $c \approx 3 \times 10^8$ m/s. The refractive index has no units).
A transparent material bound by two surfaces, of which one or both surfaces are spherical, forms a lens. 1. Convex Lens (Converging Lens): Thicker at the middle than at the edges. It converges parallel rays of light to a principal focus. 2. Concave Lens (Diverging Lens): Thicker at the edges than at the middle. It diverges parallel rays of light, making them appear to come from a principal focus.
Lenses have two centers of curvature ($C_1, C_2$) and two principal foci ($F_1, F_2$) because they have two spherical surfaces. The central point of a lens is its Optical Centre (O).
Similar to mirrors, we use ray diagrams. * Convex Lenses: Generally form real, inverted images. However, when the object is placed very close to the lens (between F and O), it forms a virtual, erect, and magnified image (used as a simple magnifying glass). * Concave Lenses: ALWAYS form virtual, erect, and diminished images.
The sign convention remains the same as for mirrors, but distances are measured from the Optical Centre (O). * The focal length of a convex lens is positive (+). * The focal length of a concave lens is negative (-).
Lens Formula: $$ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} $$
Magnification (m): $$ m = \frac{h'}{h} = \frac{v}{u} $$
The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. The power ($P$) of a lens is the reciprocal of its focal length ($f$) measured in meters. $$ P = \frac{1}{f \text{ (in meters)}} $$ * SI Unit of Power: Dioptre (D). 1 D is the power of a lens whose focal length is 1 meter. * The power of a convex lens is positive, and that of a concave lens is negative. (e.g., if an optician prescribes corrective lenses of +2.0 D, it means it is a convex lens with a focal length of +0.5m).
The study of light's behavior at boundaries allows us to manipulate it for our benefit. Reflection, governed by strict geometric laws, explains how we see ourselves in mirrors and how telescopes gather distant starlight. Refraction, caused by the changing speed of light across different media, explains optical illusions like bent pencils in water and forms the basis for how lenses focus light. By mastering the mathematical formulas for mirrors and lenses, we can design optical instruments ranging from simple spectacles to powerful microscopes and cameras.