Understanding Light: Wave and Particle Models

• Nature equipped the human eye to detect electromagnetic waves, specifically those within the 400 nm to 750 nm wavelength range, known as light.
• Light enables the sense of vision, which is crucial for understanding the surrounding world.
• Light travels incredibly fast and in a straight line. Its speed in a vacuum is a universal constant, c, approximately 3 × 108 m/s, the highest speed achievable in nature.
• Light can be understood as both a wave (electromagnetic) and a particle (ray), depending on the situation.
• A light ray is a path light travels along, and a beam of light contains light rays.
• Phenomena like light reflection, refraction, and dispersion can be studied using the concept of light rays.

Particle Model of Light

• Newton advanced the corpuscular model of light proposed by Descartes, presuming light energy is concentrated in tiny particles called corpuscles.
• The model explains reflection by particles bouncing off surfaces such as a ball bouncing off a smooth surface
• In explaining refraction, the model incorrectly postulated that light moved faster in water or glass than air.
• Newton observed phenomena like colors in thin films of oil on water.
• Partial reflection led Newton to suggest that some corpuscles are reflected while others are transmitted.

Reflection of Light by Spherical Mirrors

• The angle of incidence equals the angle of reflection. The incident ray, reflected ray, and the normal to the reflecting surface all lie in the same plane.
• Sign Conventions are followed to measure these distances, such as the Cartesian sign convention, with all distances measured from the pole of the mirror or the optical center of the lens.
• Distances in the direction of incident light are positive, opposite are negative; heights above the x-axis are positive, below are negative.
• Focal Length relates to a parallel beam of light after reflecting from a spherical mirror.
• Concave mirrors converge parallel rays at the principal focus (F), while convex mirrors diverge rays from F.
• The focal length (f) is the distance between F and the pole (P). The focal length is half the radius of curvature R, where f = R/2.
• Image Formation refers to the meeting point of reflected rays after reflection/refraction. A real image is where rays converge; a virtual image is where rays appear to diverge.

The Mirror Equation

• Two rays are needed to trace paths from a point on an object, find their intersection, and form an image.
• These rays include the ray parallel to the principal axis, reflected through the focus (or appears to diverge from the focus), the ray through (or towards) the center of curvature, reflected back along its path, and the ray through (or towards) the focus, which is reflected parallel to the principal axis.
• An incident ray at any angle at the pole is reflected.
• The mirror equation relates object distance (u), image distance (v), and focal length (f),using 1/v + 1/u = 1/f
• Magnification (m) defines the size of the image (h') relative to the object (h), expressed as m = h′/h = −v/u.
• With defined sign conventions to yield valid results.

Refraction

• Part of a light beam reflects back into the first medium when encountering another transparent one, and the rest enters the second medium. The direction of propagation changes, which is known as refraction
• Snell's Laws state the incident ray, refracted ray, and the normal are in the same plane. sin i / sin r = n21,
• The ratio of the sine of the angles of incidence i and refraction r is constant, equaling the refractive index of the second medium with respect to the first.
• If n21 > 1, medium 2 is optically denser than medium 1, causing the ray to bend towards the normal (r < i).
• If n21 < 1, the ray bends away from the normal, making medium 2 optically rarer than medium 1 (r > i)
• Lateral Shift is implied for a rectangular slab since refraction occurs between air and glass. The emergent ray is parallel to the incident ray, only shifted laterally.
• A tank filled with water appears to be raised, with the apparent depth equal to the real depth divided by the refractive index of water.
• Atmospheric refraction bends light, causing the sun to be visible before actual sunrise and after sunset.

Total Internal Reflection

• When light travels from an optically denser to a rarer medium, it is partly reflected back and partly refracted. This reflection is called internal reflection.
• At critical angle (ic), where the angle of refraction is 90º, sin ic = n₂₁
• The refractive index of denser medium 1 with respect to rarer medium 2 is n₁₂ = 1/sinic.

Total Internal Reflection Applications

• Diamonds are known for their brilliance. Their brilliance is due to total internal reflection of light inside them. The critical angle for diamond-air interface (= 24.4°) is very small, therefore, once light enters a diamond, it is very likely to undergo total internal reflection inside it.
• Prisms are designed to bend light making use of total internal reflection.
• Optical fibers are also an application. Light directed into one end undergoes repeated total internal reflections along the fiber, with negligible intensity loss, acting as an optical pipe.
• Mirage Formation occurs on hot days when air near the ground is hotter than above. Since hotter air is less dense, the effective index at different layers vary, causing total internal reflection from the ground.

Refraction at Spherical Surfaces and by Lenses

• Refraction occurs at a spherical interface:
• n2/v - n1/u = (n2 - n1)/R, with n1 and n2 representing the refractive indices of two media, u being the object distance, v the image distance, and R the radius of curvature.
• Lens Maker's Formula designs lenses of radius of curvature for focal length. The formula is 1/f = (n21 - 1)(1/R1 -1/R2).
• The power P of a lens is defined as P = 1/f. The SI unit for power is dioptre (D).

Optical Instruments

• The eye, a key optical instrument, takes in light through the cornea, controlled by the pupil's size, focusing on the retina using an eye lens.
• Accommodation is the ability of the eye to adjust focal length to focus on objects regardless of distance.
• Defects such as myopia (nearsightedness) and hypermetropia (farsightedness) can be corrected using lenses.
• A simple microscope uses magnification that achieves an object to be brought closer to the eye. The formula is m ~ D/f.
• A telescope is used to provide angular magnification. The formula is m = f0 / fe. Where the tube length is equal to f0+ fe.