Fundamental Concepts in Physics and Biology
Physics Fundamentals
Optics: Formulas and Definitions
Key Optical Formulas
- Refractive Index (Prism Formula): n = sin((A + Dₘ) / 2) / sin(A / 2)
- Displacement Formula: d = (l sin(i – r)) / cos(r)
Sign Conventions and Lens Formulas
- Object Distance (u): Always positive (+)
- Image Distance (v): Real (+) / Virtual (-)
- Magnification (m): Real (-) / Virtual (+)
- Focal Length (f) & Power (P): Convex (+) / Concave (-)
- Lens Behavior:
- If v > f: Convex lens behavior
- If v < f: Concave lens behavior
- Refraction at Spherical Surface: n₁/u + n₂/v = (n₂ – n₁)/R
- Lens-Maker’s Formula: 1/f = (n – 1) (1/R₁ – 1/R₂)
Lens Definitions
- Lens: A transparent material that can diverge or converge rays of light. A lens has at least one curved surface. There are two main types of lenses:
- Convex lens (converging lens)
- Concave lens (diverging lens)
- Principal Focus of a Convex Lens: The rays parallel to the principal axis converge at a point on the principal axis after refraction through a convex lens. This point is called the principal focus of the convex lens. Since these rays actually pass through the focus, the principal focus of a convex lens is real.
- Power of a Lens: Inversely proportional to the focal length of the lens.
Electricity: Laws and Concepts
- Coulomb’s Law: The electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
- Electric Field Intensity: The electric field intensity at a point in an electric field is the electric force acting upon a unit positive charge placed at that point.
- Non-Uniform Electric Field: If the electric field intensity varies from point to point in an electric field, such an electric field is called a non-uniform electric field.
- Uniform Electric Field: If the electric field intensity at every point is the same in magnitude and direction, such an electric field is called a uniform electric field.
- Electric Line of Force: A path along which a small positive charge will move in an electric field.
Light Phenomena
- Refractive Index using Snell’s Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is always constant. That constant is the refractive index of the medium through which the refracted ray passes.
- Total Internal Reflection: This phenomenon occurs when a light ray passes from an optically more dense medium to an optically less dense medium, and the angle of incidence is greater than the critical angle. The light in the first medium does not enter the optically less dense medium and is reflected back into the first medium for all angles of incidence greater than the critical angle.
Biology Fundamentals
Physiological Processes
- Osmoregulation: The active regulation of osmotic pressure to maintain the balance of water and electrolytes in an organism. Control of osmotic pressure is needed to perform biochemical reactions and preserve homeostasis.
Water Removal in Plants
In plants, extra water is removed by transpiration and guttation.
- Transpiration: The loss of water from the plant surface. There are three different types of transpiration, namely:
- Stomatal transpiration
- Lenticular transpiration
- Cuticular transpiration
- Guttation: The expelling of excess water or nutrients through tiny openings (hydathodes) on the tips or edges of leaves of some vascular plants, such as grasses and strawberries.
Plant Waste Products
Some plants exude tannins, acids, resins, mucilage, latex, alkaloids, oils, and gum as waste products. Plants also store wastes within their leaves or barks. These wastes are periodically removed as the leaves and barks fall off.
Biological Control and Inheritance
- Negative Feedback: A control system in which a receptor detects changes in the internal environment away from the normal state and acts to return the internal environment back to a steady state.
Patterns of Inheritance
Some well-known patterns of inheritance include:
- Dominance
- Codominance
- Incomplete Dominance
- Multiple Alleles
- Mendel’s First Law (Law of Segregation): States that during the formation of gametes, the two traits carried by each parent separate.