Optics is the study of light and how it interacts with matter. It explains why mirrors show your reflection, why a straw looks bent in a glass of water, and how eyeglasses correct vision. The field splits into geometric optics, where light travels in straight lines, and wave optics, where interference and diffraction matter.
Reflection occurs when light bounces off a surface. The angle of incidence equals the angle of reflection. This is straightforward for flat mirrors. For curved mirrors, the geometry gets more interesting. Concave mirrors focus parallel rays to a point called the focal point. Convex mirrors spread them apart. Flashlights use concave reflectors to direct the beam. Car side mirrors use convex ones to give a wider field of view.
Refraction is the bending of light when it passes from one medium to another with a different refractive index. Air has a refractive index of about 1.0003. Water is about 1.33. Glass is about 1.5. Diamond is about 2.42. The higher the index, the more light slows down and bends. Snell’s law quantifies this bending. Our Snell’s Law Calculator computes refraction angles for any pair of materials.
Total internal reflection occurs when light tries to pass from a denser to a less dense medium at too steep an angle. Instead of refracting, it reflects completely. This is the principle behind fiber optics, which carry internet data as light pulses over thousands of kilometers with minimal loss. Diamond’s high refractive index causes extensive total internal reflection, which is why diamonds sparkle so brilliantly.
Lenses use refraction to focus light. A converging lens is thicker in the middle and focuses parallel rays to a focal point. A diverging lens is thinner in the middle and spreads them. The thin lens equation, 1 over f equals 1 over d_o plus 1 over d_i, relates focal length, object distance, and image distance. Our Thin Lens Calculator solves this equation.
Cameras, telescopes, and microscopes are all combinations of lenses. A camera lens focuses light onto a sensor or film. A refracting telescope uses an objective lens to gather light and an eyepiece to magnify the image. A compound microscope uses two lenses in series for high magnification. Each of these designs follows the same basic principles of geometric optics.
Dispersion occurs because the refractive index of a material depends on wavelength. Blue light bends more than red light. This is why prisms split white light into a rainbow and why chromatic aberration occurs in cheap lenses. High-quality camera lenses use multiple elements of different glass types to correct for this effect.