How light works in physics: summary, description and characteristics. Explanation of the operation of concave and convex mirrors.
Light is an electromagnetic wave that propagates in a vacuum ; the rays that the human eye perceives are included in the frequency range between 4∙10 Hz and 8∙10 Hz .
The set of colors that make up visible light is called the spectrum , and the range of frequencies is called the visible range .
Any body that is capable of emitting electromagnetic waves is a source of light. Sources that shine with their own light can be natural or artificial. Bodies that allow light to pass through them are said to be transparent .
The propagation of light is rectilinear , which is why we speak of light rays.
Geometric optics , or ray optics, is a series of phenomena that arise from the rectilinear propagation of light:
- If a luminous point S projects its light onto an extended body M, we will see the precise shadow that portrays the shape of the body struck by the light.
- If an extended source projects its light onto a body M, a penumbra zone is formed which is reached only by the edge of the rays coming from the source.
Light is also characterized by the phenomenon of reflection, but when a surface is not completely flat the reflected rays go in different directions causing diffusion.
The human eye, when faced with a flat mirror, is unable to perceive the reflected rays because they are divergent; by prolonging the rays and fixing the intersection point, the eye will see an image called virtual, believing that the light rays come from that point and not from the real source.
Spherical mirror
A spherical mirror is a surface in the shape of a spherical cap that can have the internal, concave, or the external, convex reflecting part as its reflecting part.
The spherical mirror is characterized by:
- The center of curvature C, or the center of the spherical surface.
- The optical axis, or the axis of symmetry passing through C
- The vertex, or the point of intersection between the optical axis and the cap
- The opening angle, or angle ACB
Gauss’s approximations are hypotheses to better study the images produced which assume:
- That the opening angle must be small
- That the light rays hitting the mirror are parallel to the principal optical axis
The focus is at the midpoint of the CV segment and the length of FV is the focal distance.
The virtual focus is the point where the extensions of the reflected rays intersect.
The focal point is the length of the segment VF. It is equal to half the radius of curvature of the mirror (f) F = R/2
When we consider a point as the source it will be called the object point , and the point where the reflected rays meet will be called the image point .
Principle of reciprocity of light paths
If the image point becomes an object point, the object point will in turn become an image point (conjugate points).
If the incident ray is paraxial, its reflected ray will always intersect the point F (focus).
If the incident ray starts from C it reflects on itself and goes back along the optical axis
If the incident ray starts from a point p which is before the centre, its reflecting rays will always intersect at the point P’ which is between C and F.
If the incident ray is produced by a source P which is located between F and V the reflected rays will go in different directions and their extensions at the point P’ will result in a virtual image.
If the mirrors are convex the incident rays will always produce reflected rays with different directions and this will always result in the creation of virtual images.
When spherical mirrors do not respect Gaussian approximations, the images are blurred and distorted, causing the effect called spherical aberration, because a beam of rays no longer converges at the focus but in a larger area called the caustic.
Equation of the conjugate points of a mirror
PI generic incident ray, IC the normal, IP’ reflected ray. P’ is the image of P;
VP = p, VP’ = q, VC = R
If an object point is placed on the optical axis of a spherical mirror with radius of curvature R at a distance p from the vertex, its image will be formed at a point at a distance q from the vertex.
P, q and R are related by the following relation: 1/p + 1/q = 2/r
I= image upside down and shrunk therefore real
When a light ray meets a surface, in addition to forming a reflected ray that propagates in the first medium, another ray (refracted) is formed that propagates in the second medium according to a different direction from the incident one. The deflection angle of the refracted ray depends on the wavelength of the light, in fact if it is white in the refracted ray many colored rays will be visible, while if it is colored only one ray will be distinguishable.
But if the incident ray is perpendicular to the surface, the refracted ray will not undergo any variation.
According to the second law of refraction, the ratio between the sine of the angle i and the sine of the angle r is constant: sini/sinr = n (a constant that depends on the properties in which the media propagate and is called the relative refractive index of the second medium with respect to the first). Therefore, we can also say that sini/sinr = v / v (v is the speed in the first medium, v is the speed in the second) therefore, substituting sini/sinr for an, we can write that n = v / v
1.53 is the refractive index of glass with respect to air, the angle of incidence is greater than the angle of refraction so sini > sinr so n > 1 so the second medium is denser than the first.
The refracted ray of a light ray passing from a less dense medium to a denser medium approaches the normal, while the refracted ray of a light ray passing from a denser medium to a less dense medium recedes.
So if the light ray comes from the second medium and refracts in the second the relative refractive index becomes n = v / v therefore n = 1/n
So the absolute refractive index of a transparent medium is the ratio of the speed c of light in a vacuum to the speed v in the medium: n = c/v
Principle of reciprocity of the light path : if the angle of refraction becomes the angle of incidence, the angle of incidence becomes that of refraction.
Total reflection occurs when the angle of the incident light ray exceeds the limiting angle, that is, the angle corresponding to a refraction angle of 90° (depends on the refractive index of the medium -Lglass/air = 42°-). The refracted ray will return to the same medium if it exceeds it, while it will be equal to the surface if it is 90°. It occurs only when the light ray passes from a denser medium to a less dense medium.
Thin lenses
A lens is a transparent medium bounded by two surfaces. At least one of these surfaces must be curved with the centers of curvature on the same axis. Lenses can be :
- Thin when the thickness is negligible with respect to the axis of curvature.
- Convergent (biconvex, planoconvex, convergent meniscus) when they are thicker at the center than at the edges
- Divergent (biconcave plane concave meniscus divergent) when they are thicker at the edges and thinner at the center.
Their characteristics are:
- The centers of curvature C and C
- The optical center O, or the point where the rays pass without changing direction
- The principal optical axis, or the straight line passing through O
- The F and F fires
Having a biconvex lens, if the rays start from F they emerge parallel to AO after having passed through the lens and refracted twice; while when the incident rays are parallel to AO, after having passed through the lens they converge on F. Having a divergent lens, the incident rays emerge parallel to AO, and their extension converges on F; if the incident rays are parallel to AO they emerge divergent, and their extension converges on F.
The properties of the optical ray and the foci are valid only within the limits of Gaussian approximations, if the lenses are thin and only if the light rays are monochromatic. If the conditions are not respected, two types of aberrations (confused and distorted images) occur: chromatic , when the light source is not of a single color, spherical when the light rays are focused in different points, intersecting each other on a surface called aberration caustic.
