Ray optics, also known as geometrical optics, is a branch of physics that studies the behavior of light using the concept of light rays. It provides a simplified model for understanding how light interacts with optical elements like mirrors, lenses, and prisms, and forms the basis for designing optical instruments.
Fundamental Principles
- Rectilinear Propagation: Light travels in straight lines in a homogeneous medium.
- Reflection: When light strikes a surface, it bounces back. The angle of incidence (angle between the incident ray and the normal to the surface) equals the angle of reflection.
- Refraction: When light passes from one medium to another, it bends due to the change in speed. Snell’s law governs refraction: n₁sinθ₁ = n₂sinθ₂, where n is the refractive index of the medium and θ is the angle of incidence/refraction.
- Total Internal Reflection: When light travels from a denser medium to a rarer medium at an angle greater than the critical angle, it is completely reflected back into the denser medium.
Optical Elements
Mirrors:
- Plane Mirrors: Produce virtual, upright images that are laterally inverted.
- Spherical Mirrors:
- Concave Mirrors: Converge light rays. Can form real or virtual images depending on the object’s position.
- Convex Mirrors: Diverge light rays. Always form virtual, diminished, and upright images.
Lenses:
- Convex Lenses: Converge light rays. Can form real or virtual images.
- Concave Lenses: Diverge light rays. Always form virtual, diminished, and upright images.
Prisms: Disperse light into its constituent colors due to the variation of refractive index with wavelength.
Optical Instruments
Optical instruments use mirrors, lenses, and prisms to manipulate light and form images. Some common examples include:
- Human Eye: A complex optical system that forms images on the retina.
- Cameras: Use lenses to focus light onto a sensor or film, capturing images.
- Telescopes: Use lenses or mirrors to gather and focus light from distant objects.
- Refracting Telescopes: Use lenses.
- Reflecting Telescopes: Use mirrors.
- Microscopes: Use lenses to magnify tiny objects.
- Simple Microscopes: Use a single converging lens.
- Compound Microscopes: Use multiple lenses for higher magnification.
- Binoculars: Use prisms and lenses to provide magnified views of distant objects.
Important Concepts
- Focal Length: The distance between the optical center of a lens or mirror and its focal point.
- Magnification: The ratio of the image height to the object height.
- Power of a Lens: The reciprocal of the focal length, measured in diopters.
- Lensmaker’s Formula: Relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces.
Limitations of Ray Optics
Ray optics is a simplified model and cannot explain phenomena like diffraction and interference, which require wave optics for a complete understanding.