Electromagnetism, Optics, and Light Phenomena
Electromagnetism and Induction
Faraday’s Experiment
When a magnet’s poles approach a coil connected to a galvanometer, the galvanometer detects current. A stationary magnet produces a zero reading, and when the magnet moves away, a reverse current is detected. This involves two components: the induced (loop) and the inductor (magnet).
Henry’s Experiment
A conductor moving perpendicular to a magnetic field creates a potential difference across its ends. This potential difference induces a current if the conductor is part of a closed circuit.
Faraday’s Law
Any change in magnetic flux through a circuit creates an induced electromotive force (EMF). This EMF exists only while the flux changes and is proportional to the rate of change.
[Formula of EMF]
Lenz’s Law
The direction of the induced current opposes the change in magnetic flux that produced it. This upholds the principle of energy conservation.
[Flowchart I]
Self-Induction
Varying current in a solenoid generates a changing magnetic field, causing a flux variation. This flux variation creates an EMF and resistance that oppose the change in current.
[Formula]
Mutual Induction
Mutual induction is the appearance of an EMF in one circuit due to a current change in a nearby circuit. Transformers, based on mutual induction, convert alternating current (AC) to another AC with different current and voltage while maintaining power.
Eddy Currents
Eddy currents are electric currents induced in solid conductors when the magnetic flux passing through them varies.
Electromagnetic Waves and Spectrum
Electromagnetic Waves
Electromagnetic waves are transverse waves where electric and magnetic fields are perpendicular to each other and the direction of propagation.
Electromagnetic Spectrum
The electromagnetic spectrum encompasses all electromagnetic radiation at different frequencies. These waves propagate in a vacuum at a constant speed, independent of frequency.
Optics
Spherical Diopters
A spherical diopter is a spherical surface separating two transparent media with different refractive indices. It can be concave (R < 0) or convex (R > 0).
n’/s’ – n/s = (n’-n)/R
Mirrors
A mirror is a surface where specular reflection occurs. Its surface can be flat or spherical. Spherical diopter formulas apply, with reflection as a special case of refraction (n’ = -n).
Thin Lenses
A lens is a focusing optical system combining two diopters, at least one being spherical. Lenses are thin if their thickness is small compared to other dimensions, like radii of curvature. Lenses are classified as:
- Converging: Thicker at the center. Parallel rays converge at a focal point F’.
- Diverging: Thicker at the edges. Parallel rays diverge after refraction.
Light Phenomena
Reflection of Light
Diffuse reflection occurs when light hits an irregular surface, resulting in multiple reflections. Specular reflection occurs on a polished surface, with reflection in a single direction.
Snell’s Law
The ratio of the sines of the angles of incidence and refraction equals the ratio of propagation velocities in the media (n1 * sin i = n2 * sin r). The normal, incident ray, and refracted ray lie in the same plane.
Flat and Parallel Plate
A light beam incident on a transparent sheet with flat, parallel faces is refracted parallel on both sides. If the sheet is immersed in a medium with a different refractive index, the emergent ray is parallel to the incident ray but undergoes lateral displacement.
Prism
A prism is a transparent medium bounded by two non-parallel flat surfaces. The angle between these surfaces is the prism angle.
Light Dispersion
Light dispersion is the separation of complex light into simpler lights characterized by their wavelengths, often using a prism. When white light enters a prism, different wavelengths propagate at different speeds, separating into a continuous spectrum of colors.
Geometric Optics
Geometric optics studies light phenomena using the concept of light rays, without considering light’s electromagnetic nature. It’s based on these principles:
- Light travels in straight lines in homogeneous, isotropic media.
- A ray represents the direction of light propagation.
- Light obeys the laws of reflection and refraction.
- Light follows the shortest path (Fermat’s principle).
- Rays propagate independently.