Ray Optics: Reflection and Refraction

• Ray optics, also known as geometrical optics, describes light propagation in terms of rays.
• Rays travel in straight lines and their paths are governed by laws of reflection and refraction at interfaces between different media.
• Ray optics is an approximation valid when the wavelength of light is much smaller than the size of the objects it encounters.

Reflection

• Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.
• The law of reflection states that the angle of incidence is equal to the angle of reflection, and the incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
• Specular reflection occurs when light is reflected from a smooth surface at a definite angle.
• Diffuse reflection occurs when light is reflected from a rough surface in many different directions.

Refraction

• Refraction is the change in direction of a wave passing from one medium to another caused by its change in speed.
• The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in that medium.
• Snell's law relates the angles of incidence and refraction to the refractive indices of the two media: n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
• Total internal reflection occurs when light traveling from a medium with a higher refractive index to a medium with a lower refractive index strikes the interface at an angle greater than the critical angle.
• The critical angle is the angle of incidence for which the angle of refraction is 90 degrees.

Lenses

• A lens is a transparent optical device that refracts light to form an image.
• Convex lenses converge light rays, while concave lenses diverge light rays.
• The focal length of a lens is the distance from the lens to the point where parallel rays of light converge (for a convex lens) or appear to diverge from (for a concave lens).
• The lensmaker's equation relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces: 1/f = (n-1)(1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature of the lens surfaces.
• The thin lens equation relates the object distance (u), image distance (v), and focal length (f) of a lens: 1/f = 1/u + 1/v.
• The magnification of a lens is the ratio of the image height to the object height: m = -v/u.

Optical Instruments

• The human eye is a complex optical system that uses a lens to focus light onto the retina.
• Common vision defects include myopia (nearsightedness), hyperopia (farsightedness), and astigmatism.
• A simple microscope uses a single convex lens to magnify small objects.
• A compound microscope uses two lenses (objective and eyepiece) to achieve higher magnification.
• A telescope uses lenses or mirrors to collect and focus light from distant objects.
• Refracting telescopes use lenses to focus light, while reflecting telescopes use mirrors.