Definition of a concave mirror
One type of mirror used in everyday life is a concave mirror. A concave mirror is a curved shape mirror, where a mirror surface reflects light curves backward.
Uses of the concave mirror
If you want to observe your facial skin more clearly and in detail, close your face to the surface of a concave mirror that reflects light so that the image of your face looks bigger and the pores of the facial skin can be seen clearly. The image of your face looks bigger than your face because the mirror enlarges the image, where this happens when the distance of your face from the concave mirror is smaller than the focal length of the mirror. Because it can enlarge images, concave mirrors are usually used by women to dress up and use men when shaving.
The mirrors are also used in flashlights and car headlights. The use of a mirror on a flashlight, car headlights, or other spotlights is to parallel the light so that all light can move straight ahead. If you open the glass front cover of the flashlight and release the concave mirror, the resulting flashlight will widen in all directions and cannot illuminate objects or road surfaces at a distance.
Besides being used in flashlights or other spotlights, mirrors are also used in solar power plants. In a solar power plant, a concave mirror collects sunlight, and all light is directed towards the focal point of the mirror, where at the focal point the concave mirror is placed in a vessel. Sunlight is used to evaporate water in a vessel, where steam is used to drive electric energy-generating turbines.
The focal point of the concave mirror
If the surface of a concave mirror that reflects light is exposed to a very distant object such as the sun, then the beam of light emitted by the sun will parallel with the principal axis of the concave mirror, as shown in the figure below. The principal axis is an imaginary straight line perpendicular to the center of the surface of the concave mirror. In the figure below, the principal axis lines coincide with the point of the intersection of all reflected light rays.
When strikes the surface of the concave mirror, each beam of light obeys the law of reflection of light. Between the incident light rays and the reflected light rays, there is a normal line perpendicular to the mirror surface that is passed by the light ray, but the normal line is not shown.
The angle between the incident light rays with the normal line is the same as the angle between the reflected light beams and the normal line. Unlike a plane mirror that has a flat surface so that all normal lines are in the same direction, the normal line of the concave mirror is not unidirectional because the concave mirror surface is curved and not flat. All the reflected rays intersect at one point that coincides with the principal axis called the focal point (F). In other words, the focal point is the image point of an object that is very far from the surface of a concave mirror, such as the sun and stars.
Based on the law of reflection of light, the direction of the beam of light or the ray of light can be reversed, in contrast to the previous image. If assumed that a light source is at the focal point of the concave mirror, the beam of light emitted by the object reflected by the surface of the concave mirror. The direction of the reflected light beam is parallel to the principal axis of the concave mirror. This is the fundamental principle behind the use of concave mirrors on flashlights, car headlights, or other spotlights, the use of concave mirrors in solar power plants.
Based on the explanation above, can be concluded that if there is a light source located at the focal point of the concave mirror, the beam of light emitted by the object is reflected by the surface of the concave mirror where the reflected light beam is parallel to the principal axis of the concave mirror. Conversely, if the object is at a great distance, the image of the object is at the focal point of the concave mirror. If a very distant object has an image at the focal point, where is the image of the object if the distance of the object from the surface of the mirror is finite or near? To understand this, please learn the topic of image formation by the concave mirror.
The focal length of the concave mirror
Focal length (f) is the distance between the focal point (F) and the concave mirror surface. The following is explained how to determine the focal length of a concave mirror using the incident light rays and the reflected light rays.
Point C is the center of the concave mirror curvature. The focal length of the concave mirror is f (focal length = f = FQ), and the radius of the curvature of the concave mirror is r (curvature radius = r = CQ = CP).
The incident light rays strike the concave mirror on P then is reflected towards the focal point F. The dashed line CP is the normal line. The incoming light rays and reflected light rays fulfill the law of reflection of light where the angle of incidence (θ) is equal to the angle of reflection (θ) and this angle is equal to the angle of the triangle PCQ (θ). The triangle angle of PCQ is the same as the angle of the triangle CPF. Therefore the PFC triangle is an equilateral triangle. Because the PFC triangle is an equilateral triangle, the length of the PF equals the length of the CF. Assuming the mirror width is smaller than the radius of the mirror curvature, the length of the PF is considered equal to the length of the FQ. Because CF = PF and PF = FQ then CQ = 2 CF = 2 FQ. CQ = r = the radius of the curvature of the concave mirror and FQ = f = focal length of the concave mirror. Thus can be concluded that the radius of curvature of the concave mirror (r) = 2 x the focal length (f) of the concave mirror. Mathematically :
r = 2f or f = r / 2
Image formation by the concave mirror
Plane mirrors can only form the virtual image while the concave mirrors can form the real image and the virtual image. The image of an object is real or virtual depending on the distance of the object from the surface of the concave mirror and this has been explained in detail in the topic of the image formation by the concave mirror.
An image is real if the reflected light beam crosses the point where the image is located. If a screen is placed in a position where there is a real image, it will appear a light beam on the screen, and this beam of light has the shape of an object. The existence of real images formed by the concave mirrors is the reason why the concave mirrors are used in astronomical telescopes. On the topic of the lens, you will know that the ability of a lens to form a real image is the reason for the use of the lens on the optical telescope.
An image is virtual if the reflected light beam does not pass through the point where the image is located. If a screen is placed in a position where there is a virtual image, there is no visible light beam on the screen. The virtual image doesn’t exist, but the human eye sees a beam of light moving in a straight path so that it looks as if the light is moving straight from the point where the image is.