## Electromagnetic Spectrum ### Fields A field is something defined everywhere in space that determines how objects interact without direct contact. In physics, the classical fields are: - Gravitational field - Electric field - Magnetic field Electricity and Magnetism are related forms of interaction, and combined form electromagnetic waves. #### Gravitation Fields In general, objects generate a field in the surrounding space, and that field exerts a force on similar objects in the space. Any mass creates a force field in the surrounding space called the gravitational field. From Newton's theory of gravitation, the force $F$ between two masses $m_{1}$ and $m_{2}$, separated by distance $r$ is $ F=-G \frac{m_{1}m_{2}}{r^2} $ Where $G$ is the gravitation constant. #### Electric Fields There are two types of electric charge, positive and negative. Atoms contain protons (positively charged) and electrons (negatively charged). Particles with the same electric charge repeal, while particles with opposite charge attract. A charged object creates an electric field, even in a vacuum. A charged particle placed in an electric field experiences an electrostatic force. The electric field at a point in space is quantified by the force that would be exerted on a small positive test charge located at that point. #### Magnetic Fields Electrons have an intrinsic magnetic field around them. In certain materials, the magnetif fields of the electrons produce a net magnetic field for the entire material. This is called a permanent magnet. Alternatively, an electric current in a a wire produces a magnetic field. This is called an electromagnet. A charged particle moving in a magnetic field experiences a magnetic force (the force is zero if the particle is stationary). The magnitude of the magnetic force is proportional to the charge and velocity of the particle. ### Electromagnetism Electricity and magnetism are a connected phenomena. Electric fields and magnetic fields both exert forces on a charged particle. An electric current in a wire can set up a magnetic field, and a changing magnetic field may induce an electric current (electromagnetic induction). In general, a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. #### Electromagnetic Waves > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://chem.libretexts.org/Courses/Furman_University/CHM101:_Chemistry_and_Global_Awareness_(Gordon)/05:_Basics_of_Nuclear_Science/5.02:_The_Electromagnetic_Spectrum) licensed under [CC-BY-SA-NC](https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en) The changes in the magnetic and electric fields do not occur instantaneously everywhere in the surrounding space. These changes travel outwards from the “source” in the form of Electromagnetic (EM) Waves. EM waves are oscillations of electric and magnetic fields that propagate through space. The oscillations in the electric and magnetic fields are sinusoidal, in phase, and perpendicular to each other and to the direction of travel. Thus, EM waves are transverse. Although the planes containing the electric and magnetic fields are always perpendicular, their orientation varies randomly as the waves propagate, unless the EM waves are polarised. EM waves can propagate through a medium or a vacuum. In a vacuum the wave speed $c \approx 3.0 \times 10^8 \text{ms}^{-1}$. The ratio of wave speed in a vacuum $c$ to the wave speed in a medium $v$ us called the absolute index of refraction and is given by $n=\frac{c}{v}$. #### Electromagnetic Spectrum > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://chem.libretexts.org/Courses/Sacramento_City_College/SCC%3A_CHEM_300_-_Beginning_Chemistry/SCC%3A_CHEM_300_-_Beginning_Chemistry_(Alviar-Agnew)/09%3A_Electrons_in_Atoms_and_the_Periodic_Table/9.03%3A_The_Electromagnetic_Spectrum) licensed under [CC-BY-SA-NC](https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en) The range of EM waves is called the Electromagnetic Spectrum. In a vacuum, all EM waves travel at the same speed $c$. In waves, the frequency $f$ (Hz) and wavelength $\lambda$ (m) are related to the wave speed $c$ by $c=f\lambda$. The wavelengths of EM waves have no lower or upper bound. | Type | Wavelength range | Frequency range | | ------------ | -------------------------------------- | ----------------------------------------------------------- | | Gamma rays | $\lambda <1\text{ nm}$ | $f>3\times 10^{17}\text{ Hz}$ | | X-rays | $\lambda<1\text{ nm}$ | $f>3\times 10^{17}\text{ Hz}$ | | Ultra-voilet | $1\text{ nm}<\lambda <400\text{ nm}$ | $3\times 10^{17}\text{ Hz}<f<7.5\times 10^{14}\text{ Hz}$ | | Light | $400\text{ nm}<\lambda <700\text{ nm}$ | $7.5\times 10^{14}\text{ Hz}<f<4.3\times 10^{14}\text{ Hz}$ | | Infra-red | $700\text{ nm}<\lambda <1\text{ mm}$ | $4.3\times 10^{14}\text{ Hz}<f<3\times 10^{11}\text{ Hz}$ | | Microwaves | $1\text{ mm}<\lambda <0.1\text{ m}$ | $3\times 10^{11}\text{ Hz}<f<3\times 10^{9}\text{ Hz}$ | | Radio waves | $\lambda>0.1\text{ m}$ | $f<3\times 10^{9}\text{ Hz}$ | ### Wavefronts & Rays - Wavefront is an imaginary surface where the wave has the same phase - Rays are imaginary lines that are perpendicular to wavefronts and show the direction of propagation of the wave In many circumstances, straight light rays can be used to model the path of light A plane wave is an idealised wave with planar wavefronts, which travel in a single direction. Although a plane wave is a one-dimensional wave, plane waves can be used to model some three-dimensional waves a large distance from the source. For example, spherical wavefronts from a point source can be modelled locally as plane waves a large distance from the source. ## Reflection > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://pressbooks.bccampus.ca/introductorygeneralphysics2phys1207opticsfirst/chapter/25-2-the-law-of-reflection/) licensed under [CC-BY]([https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en](https://creativecommons.org/licenses/by/4.0/deed.en)) Reflection of light is when light reflects off a surface. Depending on the type of surface, the light energy can be reflected, transmitted (into the material) and/or absorbed (converted to another form - usually heat). ### Reflectivity The reflectivity of a surface quantifies the proportion of the incident energy that is reflected. $ \text{Reflectivity}=\frac{\text{Reflected energy}}{\text{Incident energy}} $ A perfect reflector has a reflectivity of $1$. All the energy is reflected. A perfect non-reflector has a reflectivity of $0$. All the energy is absorbed. ### Specular vs Diffuse Reflection > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://k12.libretexts.org/Bookshelves/Science_and_Technology/Physics/14:_Optics/14.01:_Reflection) licensed under [CC-BY-SA-NC](https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en) Specular reflection occurs when a reflector is “smooth”. On a “smooth” surface, the lengthscale of any surface roughness is less than the wavelength of light. Specular reflection is “mirror-like” reflection. Incident waves at a specific angle are reflected at a single, predictable direction. Diffuse reflection occurs when a reflector is “rough”. On a “rough” surface, the roughness lengthscale is comparable or greater than the wavelength of light. Diffuse reflection is when incident waves are reflected in many directions. The reflected energy spreads out, and the light is scattered in multiple directions. ### Law of Reflection For a specular reflector, the incident ray, reflected ray, and normal to the surface all lie in the same plane. The angle of reflection is the same as the angle of incidence. $ \theta_{i}=\theta_{r} $ ### Plane Mirrors > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://courses.lumenlearning.com/physics/chapter/25-2-the-law-of-reflection/) licensed under [CC-BY]([https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en](https://creativecommons.org/licenses/by/4.0/deed.en)) A mirror is a specular reflector. Consider a point source of light located at point O, a perpendicular distance $d$ from the mirror. If your eyes intercept the reflected rays, you perceive that point source is located behind the mirror at point $I$. This is called a virtual point image. The virtual point image is located a perpendicular distance $d$ behind the mirror. Now consider an object (not a point source). The object can be viewed as a composite of many smaller elements, each which can be treated as a point source. If your eyes intercept the reflected rays, you perceive the the object is behind the mirror. This is called a virtual image. It is a composite of all the virtual point images. ### Spherical Mirrors A spherical mirror is a mirror whose reflective surface is a part of a sphere. The radius of the sphere $r$ is known as the radius of curvature. A spherical mirror with a very large radius of curvature is locally approximately flat. A concave spherical mirror curves inwards, while a convex spherical mirror curves outward. #### Focal Points > [!figure] ![[Screenshot 2026-03-16 at [email protected]]] > [Unknown Author](https://k12.libretexts.org/Bookshelves/Science_and_Technology/Physics/14:_Optics/14.05:_Concave_Mirrors) licensed under [CC-BY-SA-NC](https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en) Parallel rays reflected by a concave mirror intersect at a focal point. The distance along the principle axis from the mirror to the focal point is called the focal length $f$. The radius of the sphere is the radius of curvature. For a spherical mirror: $ f=\frac{1}{2}r $ ## Refraction Refraction of light occurs when light changes speed passing from one transparent medium to another. Owing to refraction, light rays change direction passing from one transparent medium to another. ![[Screenshot 2026-03-16 at [email protected]]] The end of the pencil is at X. However, if your eyes intercept the reflected rays, you perceive that the end of the pencil is at Y. This is caused by refraction of the light at the air-water interface. It occurs because the wave speed (speed of light) in air is different to in water. ![[Screenshot 2026-03-16 at [email protected]]] Consider a plane wave incident at the interface between two media at an oblique angle. Assume that the wave propagates from a less dense to a more dense optical medium. For a ray of light, the wave speed decreases in a denser optical medium. Consequently, as a wavefront reaches the interface, the first "end" will slow down. This causes the direction of the wavefronts to rotate, known as refraction. ### Huygen's Principle Christiaan Huygens developed a wave theory for light that can explain effects such as reflection and refraction. What is now known as Huygen’s principle uses a geometrical construction to determine the future position of a wavefront if its present position is known. In simple terms, the principle asserts that every point on a wavefront acts as a point source of spherical secondary wavelets. Visualise the secondary wavelets spreading outwards at the same speed as the wave. A short time later, the new wavefront is the surface that is tangential to all the secondary wavelets. ![[Screenshot 2026-03-16 at [email protected]]] This principle can be used to derive Snell's Law. ### Snell's Law Snell's law determines how the ray angles $\theta_{1}$ and $\theta_{2}$ are connected to wave speeds $v_{1}$ and $v_{2}$ of the media. The ray angles are measured relative to the normal between the two media. ![[Screenshot 2026-03-16 at [email protected]]] Consider the wavefront highlighted in red. The part of the wavefront that remains in medium 1 travels a distance $v_{1}t$ in time $t$. The part of the wavefront that propagates into medium 2 travels a distance of $v_{2}t$ in the same time. A Huygen's secondary wavelet that originates on the interface at point A is shown. Since the rays are perpendicular to the wavefronts, now consider the right angle triangles ACB and BDA. Note the lengths and angles: $ BC=v_{1}t \qquad \angle BAC=\theta_{1} \qquad AD=v_{2}t \qquad \angle ABD=\theta_{2} $ ![[Screenshot 2026-03-16 at [email protected]]] From trigonometry: $ AB \sin\theta_{1}=v_{1}t \qquad AB \sin\theta_{2}=v_{2}t \qquad \frac{AB\sin\theta_{1}}{AB\sin\theta_{2}}=\frac{v_{1}t}{v_{2}t} $ Finally, simplifying gives Snell's law: $ \boxed{\frac{\sin\theta_{1}}{\sin\theta_{2}}=\frac{v_{1}}{v_{2}}} $ ### Index of refraction The speed of light is dependent on the medium the light is travelling through. For light, the index of refraction (or refractive index) is the non-dimensional ratio: $ n=\frac{c}{v} $ Where $c$ is the speed of light in a vacuum and $v$ is the speed of light in a medium. Noting that $v<c$, the index of refraction $n>1$. Snell's law can be rewritten in terms of the index of refraction: $ n_{1}=\frac{c}{v_{1}}\qquad n_{2}=\frac{c}{v_{2}} \qquad \frac{v_{1}}{v_{2}}=\frac{n_{2}}{n_{1}} \qquad \boxed{\frac{\sin\theta_{1}}{\sin\theta_{2}}=\frac{n_{2}}{n_{1}}} $ ![[Screenshot 2026-03-16 at [email protected]]]