Geometrical Optics
Geometrical optics describes how light travels in straight lines. It treats light as rays rather than waves. This approach works well when the wavelength of light is much smaller than the size of the objects it encounters. Therefore, engineers and scientists use it to design lenses, mirrors, and many optical instruments.
Light rays follow simple rules when they strike a surface. They reflect at an angle equal to the angle of incidence. In addition, they change direction when they pass from one transparent medium into another. This bending is called refraction. Snell’s law governs the exact change in direction. As a result, the ray slows down or speeds up depending on the optical density of the new material.
Mirrors produce images through reflection. A plane mirror forms a virtual image that appears the same size as the object. Curved mirrors behave differently. Concave mirrors can focus parallel rays to a single point. Convex mirrors spread the rays outward. Consequently, they produce smaller virtual images and offer a wider field of view.
Lenses bend light through refraction. Convex lenses converge parallel rays toward a focal point. They form real images that can be projected onto a screen. Concave lenses diverge the rays. They produce only virtual images. In both cases, the lens maker’s equation relates the focal length to the radii of curvature and the refractive index of the glass.
The thin-lens equation connects object distance, image distance, and focal length. When the object lies beyond the focal point of a convex lens, a real and inverted image appears. When the object moves inside the focal length, the image becomes virtual and upright. Therefore, the same lens can serve different purposes depending on the object’s position.
Geometrical optics also explains optical instruments. Microscopes use combinations of lenses to magnify small objects. Telescopes gather light from distant sources and form enlarged images. Cameras control the path of rays with adjustable lenses to focus light onto a sensor. In each case, ray diagrams help predict image location and size.
This model ignores interference and diffraction. Those effects become important only when apertures or obstacles approach the wavelength of light. For most everyday applications, however, the ray picture remains accurate and practical. As a result, geometrical optics continues to guide the design of eyeglasses, cameras, and many other devices.