Lesson Notes By Weeks and Term v3 - Senior Secondary 2
Light waves
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Light waves
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Subject: Physics
Class: Senior Secondary 2
Term: 1st Term
Week: 7
Theme: Waves-Motion Without Material Transfer
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Students should beable to list some lightsources the ycome across in everyday life. determine the angle of reflection for agiven angle of incidence. draw raydiagrams to show the formation of images by planeand curvedmirrors; explain somepracticalapplications of plane and curved mirrors. explain how the direction of lightchanges as ittravels from on emedium in to the other. measureangles of incidence and refraction and:hence deducea value for the refractive.in dex of agiven materal Explain the meaning of critical angleand to talinternalreflectionstating the conditionsunder whichthey occur.
2. 1. Nature and Sources of Light Nature of Light: Light is a form of electromagnetic radiation, meaning it does not require a material medium for its propagation. It travels as transverse waves and exhibits wave-particle duality (behaving as both a wave and a stream of particles called photons). The speed of light in a vacuum (c) is approximately 3.0 x 108 m/s.
Rectilinear Propagation of Light: Light travels in straight lines in a uniform medium. Evidence includes the formation of sharp shadows and the operation of a pinhole camera.
Sources of Light (Objective 1): Luminous Sources: Objects that produce their own light.
Examples: The Sun, stars, electric bulbs, candles, kerosine lamps, fireflies (e.g., Omomgolo in some Nigerian dialects), burning firewood.
Non-luminous Sources: Objects that do not produce their own light but reflect light from luminous sources.
Examples: The Moon, planets, mirrors, human beings, furniture, books. 2.
2. Reflection of Light Definition: Reflection is the bouncing back of light rays when they strike a surface.
Laws of Reflection:
1. The incident ray, the reflected ray, and the normal (an imaginary line perpendicular to the surface at the point of incidence) all lie in the same plane.
2. The angle of incidence (i) is equal to the angle of reflection (r). (i = r) (Objective 2)
Types of Reflection: Regular/Specular Reflection: Occurs when light reflects from a smooth, polished surface (e.g., plane mirror), producing a clear image.
Irregular/Diffuse Reflection: Occurs when light reflects from a rough surface (e.g., wall, cloth), scattering light in various directions, which allows us to see objects from different angles. 2.2.
1. Reflection by Plane Mirrors Image Formation: A plane mirror always forms a virtual, upright (erect), laterally inverted, and same-size image that appears to be as far behind the mirror as the object is in front. Ray Diagram for Plane Mirror (Objective 3): Draw the object (e.g., an arrow) in front of the mirror. Draw two rays from the top of the object to the mirror surface. Apply the laws of reflection to reflect these rays. Extend the reflected rays backward (as dashed lines) until they intersect behind the mirror. This intersection point forms the image of the top of the object. Repeat for the bottom of the object if needed. 2.2.
2. Reflection by Curved (Spherical)
Mirrors Types: Concave Mirror (Converging Mirror): Reflecting surface curves inward, like the inside of a spoon. It converges parallel rays of light to a focal point.
Convex Mirror (Diverging Mirror): Reflecting surface curves outward, like the back of a spoon. It diverges parallel rays of light, making them appear to come from a virtual focal point behind the mirror.
Terminology: Pole (P): The geometric centre of the mirror's reflecting surface.
Principal Axis: The straight line passing through the pole and the centre of curvature.
Centre of Curvature (C): The centre of the sphere of which the mirror is a part. For a concave mirror, C is in front; for a convex mirror, C is behind.
Radius of Curvature (R): The distance from the pole to the centre of curvature (PC). R = 2f.
Principal Focus (F): The point on the principal axis where parallel rays of light converge after reflection (concave) or appear to diverge from after reflection (convex).
Focal Length (f): The distance from the pole to the principal focus (PF). f = R/
2. Ray Rules for Spherical Mirrors:
1. A ray parallel to the principal axis passes through the principal focus (concave) or appears to come from the principal focus (convex) after reflection.
2. A ray passing through the principal focus (concave) or directed towards the principal focus (convex) becomes parallel to the principal axis after reflection.
3. A ray passing through the centre of curvature (concave) or directed towards the centre of curvature (convex) reflects back along its original path.
4. A ray directed towards the pole reflects such that the angle of incidence equals the angle of reflection. * Image Formation by Curved Mirrors (Objective 3): Students should practice drawing ray diagrams for appears to come from the principal focus (convex) after reflection.
2. A ray passing through the principal focus (concave) or directed towards the principal focus (convex) becomes parallel to the principal axis after reflection.
3. A ray passing through the centre of curvature (concave) or directed towards the centre of curvature (convex) reflects back along its original path.
4. A ray directed towards the pole reflects such that the angle of incidence equals the angle of reflection. Image Formation by Curved Mirrors (Objective 3): Students should practice drawing ray diagrams for different object positions for both concave and convex mirrors to determine the nature, size, and position of images.
Concave Mirror: Image characteristics vary depending on object position (e.g., real, inverted, magnified/diminished/same size). When the object is between F and P, the image is virtual, erect, and magnified.
Convex Mirror: Always forms a virtual, erect, and diminished image between P and F behind the mirror.
Mirror Formula and Magnification: `1/f = 1/u + 1/v` where: f = focal length u = object distance v = image distance `M = h'/h = -v/u` where: M = magnification h' = image height h = object height Sign Convention (Cartesian Convention): Distances measured in the direction of incident light are positive (+). Distances measured opposite to the direction of incident light are negative (-).
Focal length (f): Concave mirror (+), Convex mirror (-).
Object distance (u): Always negative if real object (-).
Image distance (v): Real image (-), Virtual image (+).
Height: Upright (+), Inverted (-). Practical Applications of Plane and Curved Mirrors (Objective 4): Plane Mirrors: Dressing mirrors, periscopes (e.g., for viewing over crowds at a sallah procession or market), kaleidoscopes, optical instruments.
Concave Mirrors: Shaving mirrors (magnified image), dentist's mirrors (magnified view of teeth), headlamps of cars (produce parallel beam), solar concentrators (e.g., in rural Nigeria for cooking or water heating), searchlights.
Convex Mirrors: Rear-view mirrors in vehicles (wider field of view, diminished image), security mirrors in shops and banks (wide field of view to monitor customers/premises), street light reflectors, blind spot mirrors. 2.
3. Refraction of Light Definition: Refraction is the bending of light rays as they pass from one transparent medium to another of different optical density. (Objective 5) This change in direction occurs because the speed of light changes as it enters a new medium.
Laws of Refraction (Snell's Law):
1. The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
2. For a given pair of media and a given colour of light, the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant, called the refractive index (n). `n = sin i / sin r` Refractive Index (n): It is a measure of how much a medium can bend light. A higher 'n' means greater bending and a slower speed of light in that medium. `n = c / v`, where c = speed of light in vacuum, v = speed of light in the medium.
Relative Refractive Index: `n12 = n2 / n1 = v1 / v2` (refractive index of medium 2 with respect to medium 1). `n = Real depth / Apparent depth` (e.g., a coin at the bottom of a bowl of water appears shallower). Measurement of Angles and Refractive Index (Objective 6): Practical Method (using a rectangular glass block):
1. Place a rectangular glass block on a white sheet of paper.
2. Trace the outline of the block.
3. Draw a normal at a point on one side of the block.
4. Draw an incident ray at a known angle (i) to the normal.
5. Place two pins (P1, P2) on the incident ray.
6. Look through the opposite side of the block and place two more pins (P3, P4) such that they appear to be in a straight line with P1 and P2.
7. Remove the block and pins. Draw Place a rectangular glass block on a white sheet of paper.
2. Trace the outline of the block.
3. Draw a normal at a point on one side of the block.
4. Draw an incident ray at a known angle (i) to the normal.
5. Place two pins (P1, P2) on the incident ray.
6. Look through the opposite side of the block and place two more pins (P3, P4) such that they appear to be in a straight line with P1 and P2.
7. Remove the block and pins. Draw a line connecting P3 and P4 to represent the emergent ray.
8. Draw the refracted ray inside the block by connecting the point of incidence to the point of emergence.
9. Measure the angle of incidence (i) and the angle of refraction (r) using a protractor.
1
0. Calculate `n = sin i / sin r`. Repeat for various angles of incidence and find the average 'n'.
Observations: Light bends towards the normal when passing from a rarer medium (air) to a denser medium (glass/water), and away from the normal when passing from denser to rarer.
Parallel Displacement: For a rectangular block, the emergent ray is parallel to the incident ray but laterally displaced. 2.
4. Critical Angle and Total Internal Reflection (TIR)
Critical Angle (c) (Objective 7): When light travels from a denser medium to a rarer medium, it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°. At this angle, the refracted ray grazes the interface. Total Internal Reflection (TIR) (Objective 7): When the angle of incidence in the denser medium exceeds the critical angle, light is no longer refracted into the rarer medium. Instead, all the light is reflected back into the denser medium. This phenomenon is called Total Internal Reflection.
Conditions for TIR (Objective 7):
1. Light must travel from an optically denser medium to an optically rarer medium.
2. The angle of incidence in the denser medium must be greater than the critical angle for that pair of media. Relationship between Critical Angle and Refractive Index (Objective 8): From Snell's Law, `n_denser sin c = n_rarer sin 90°` If the rarer medium is air (n_air ≈ 1), then `n_denser sin c = 1 1` Therefore, `sin c = 1 / n_denser` (where n_denser is the refractive index of the denser medium with respect to air). This formula can be applied to solve simple problems.
Applications of TIR (Objective 8): Optical Fibres: Used for high-speed data transmission (e.g., internet, telephone lines) across Nigeria, medical endoscopes. Light signals travel through the fibre by repeated TI
R. Periscopes and Binoculars: Use prisms to achieve 90° or 180° deviation of light using TIR, which is more efficient than mirrors.
Diamond Sparkle: The high refractive index and small critical angle of diamond lead to multiple internal reflections, causing it to sparkle.
Road Reflectors (Cat's Eyes): Use TIR for visibility at night. 2.
5. Refraction through a Triangular Prism Deviation: When a monochromatic (single colour) light ray passes through a triangular prism, it deviates from its original path. It always bends towards the base of the prism.
Angle of Deviation (D): The angle between the incident ray and the emergent ray. Minimum Deviation (D_min) (Objective 9): As the angle of incidence (i) changes, the angle of deviation (D) also changes. There is a specific angle of incidence for which the angle of deviation is minimum. This is the angle of minimum deviation (D_min). At minimum deviation, the ray inside the prism is parallel to the base of the prism, and `i1 = i2` (angle of incidence = angle of emergence), and `r1 = r2`. Tracing Light Rays through a Prism (Objective 9):
1. Place the prism on a white paper and trace its outline.
2. Draw a normal at a point on one face of of deviation (D) also changes. There is a specific angle of incidence for which the angle of deviation is minimum. This is the angle of minimum deviation (D_min). At minimum deviation, the ray inside the prism is parallel to the base of the prism, and `i1 = i2` (angle of incidence = angle of emergence), and `r1 = r2`. Tracing Light Rays through a Prism (Objective 9):
1. Place the prism on a white paper and trace its outline.
2. Draw a normal at a point on one face of the prism.
3. Draw an incident ray at an angle 'i' (e.g., 40°, 45°, 50°, etc.).
4. Place two pins on the incident ray.
5. Look through the opposite face and place two more pins such that they are in line with the first two.
6. Remove the pins and prism. Draw the emergent ray.
7. Draw the incident ray and emergent ray to intersect, forming the angle of deviation (D).
8. Repeat for several angles of incidence.
9. Plot a graph of D vs. i. The lowest point on the graph gives the angle of minimum deviation (D_min).
Refractive index of prism material: `n = sin[(A + D_min)/2] / sin(A/2)` where A is the angle of the prism. 2.
6. Dispersion of Light Definition: Dispersion is the phenomenon where white light splits into its constituent colours when it passes through a prism or similar refracting medium.
Spectrum of White Light (Objective 10): The band of colours produced is called the visible spectrum, arranged in order of decreasing wavelength (and increasing frequency/energy): Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).
Cause: Different colours of light have slightly different speeds in a medium (except vacuum). This means they have different refractive indices for the same medium. Violet light bends the most (slowest speed), and Red light bends the least (fastest speed).
Natural Phenomenon: Rainbows are a result of dispersion and total internal reflection of sunlight by water droplets in the atmosphere after rain. 2.
7. Electromagnetic Spectrum Solar Energy Received by Earth (Objective 11): The Sun emits a wide range of electromagnetic radiation. The Earth's atmosphere filters much of this radiation, but a significant portion reaches the surface, including: Ultraviolet (UV)
Radiation: Higher energy than visible light. Can cause sunburn, skin cancer, but also aids in Vitamin D production. Mostly absorbed by the ozone layer.
Visible Light: The portion of the spectrum detectable by the human eye (ROYGBIV). Essential for vision, photosynthesis.
Infrared (IR)
Radiation: Lower energy than visible light. Perceived as heat. Used in remote controls, thermal imaging, and a significant contributor to the greenhouse effect, warming the Earth.
Applications: Solar panels convert visible and some UV/IR light into electricity, crucial for off-grid communities and sustainable energy in Nigeria. 2.
8. Lenses Definition: A lens is a transparent optical device made of glass or plastic, with one or both surfaces curved, that refracts light to form images.
Types: Converging Lens (Convex Lens): Thicker at the centre, thinner at the edges. Converges parallel rays of light to a real focus.
Diverging Lens (Concave Lens): Thinner at the centre, thicker at the edges. Diverges parallel rays of light, making them appear to come from a virtual focus.
Terminology: Optical Centre (O): The central point of the lens. Rays passing through O are undeviated.
Principal Axis: The straight line passing through the optical centre and the centres of curvature of the lens surfaces.
Principal Focus (F): For a converging lens, it's the point where parallel rays converge after refraction. For a diverging lens, it's the point from which parallel rays appear to diverge. Each lens has two principal foci (F1 and F2), equidistant from
O. Focal Length (f): The distance from the optical centre to the principal focus. 2F (or C): A point at twice the focal length from the optical centre. Analogous to the centre of curvature for mirrors. * Ray Rules for Lenses:
1. A ray parallel to the principal axis passes through the principal focus (converging) or appears to come from the principal
Solar Energy in Nigeria: The principles of light absorption and reflection are fundamental to solar energy technology. Students can relate the concept of solar radiation (Objective 11) to the widespread adoption of solar panels in Nigeria for electricity generation, especially in rural areas lacking grid access, and for powering streetlights and boreholes in urban centres. This connects physics to sustainable development and economic empowerment. Optical Communication and Internet Connectivity: Total Internal Reflection (TIR) is the bedrock of fibre optic technology. In Nigeria, the expansion of internet and telecommunication networks heavily relies on fibre optic cables laid across the country. Students can understand how these cables transmit light signals (data) over long distances without significant loss, enabling faster internet access and mobile communication, impacting education, business, and social interaction.
Vision Correction and Everyday Optics: Lenses (Objective 12, 13) are crucial for correcting common vision defects like myopia (nearsightedness) and hyperopia (farsightedness), conditions prevalent in Nigerian communities. Understanding how spectacle lenses work helps students appreciate the direct application of physics in improving quality of life.
Furthermore, mirrors are ubiquitous in Nigerian society, from vehicle rear-view mirrors and security mirrors in bustling markets (Objective 4) to simple dressing mirrors in homes.