Rules of Reflection


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Rule 1: After reflection, a ray of light parallel to the principal axis appears to be coming from focus. Rule 2: A ray of light going towards centre of curvature is reflected back along the same path. Rule 3: After reflection, a ray of light going towards the focus becomes parallel to the principal axis. Rule 4: Ray of light which is incident at the pole is reflected back making the same angle with the principal axis. Case 1: When the object is placed anywhere between pole and infinity between P and infinity , the image formed is:behind the mirror between P and F, virtual and erect, diminished.

Case 2: When the object is placed at infinity at infinity , the image formed is:behind the mirror at F, virtual and erect, highly diminished. New Cartesian Sign Convention is used for measuring the various distances in the ray diagrams of spherical mirrors. According to New Cartesian Sign Convention:.

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The Object is always placed on the left side of the mirror so that the direction of incident light is from left to right. Since the incident light always goes from left to right, all the distances measured from the pole of mirror to the right side will be considered positive. And on the other hand all the distances measured from pole of mirror to the left side will be negative.

A formula which gives the relationship between image distance v , object distance u and focal length f of a spherical mirror.


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The ratio of the height of image to the height of object is known as linear magnification. Height of object h 1 will always be positive. The height h 2 of a virtual image will be positive and that of real image will be negative. In other words, if the magnification has a plus sign, then the image is virtual and erect and if the magnification has a minus sign, then the image is real and inverted.

Also, the linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance, with a minus sign. School Board. These two angles are labeled with the Greek letter "theta" accompanied by a subscript; read as "theta-i" for angle of incidence and "theta-r" for angle of reflection. The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.

It is common to observe this law at work in a Physics lab such as the one described in the previous part of Lesson 1.


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To view an image of a pencil in a mirror, you must sight along a line at the image location. As you sight at the image, light travels to your eye along the path shown in the diagram below. The diagram shows that the light reflects off the mirror in such a manner that the angle of incidence is equal to the angle of reflection. It just so happens that the light that travels along the line of sight to your eye follows the law of reflection.

The reason for this will be discussed later in Lesson 2. If you were to sight along a line at a different location than the image location, it would be impossible for a ray of light to come from the object, reflect off the mirror according to the law of reflection, and subsequently travel to your eye.

Only when you sight at the image, does light from the object reflect off the mirror in accordance with the law of reflection and travel to your eye. This truth is depicted in the diagram below. For example, in Diagram A above, the eye is sighting along a line at a position above the actual image location.

For light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is less than the angle of reflection. In Diagram B above, the eye is sighting along a line at a position below the actual image location. In this case, for light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is more than the angle of reflection.

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Neither of these cases would follow the law of reflection. In fact, in each case, the image is not seen when sighting along the indicated line of sight. It is because of the law of reflection that an eye must sight at the image location in order to see the image of an object in a mirror. This is called diffuse reflection. The exact form of the reflection depends on the structure of the material. One common model for diffuse reflection is Lambertian reflectance , in which the light is reflected with equal luminance in photometry or radiance in radiometry in all directions, as defined by Lambert's cosine law.

The light sent to our eyes by most of the objects we see is due to diffuse reflection from their surface, so that this is our primary mechanism of physical observation.

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Reflections

Some surfaces exhibit retroreflection. The structure of these surfaces is such that light is returned in the direction from which it came. When flying over clouds illuminated by sunlight the region seen around the aircraft's shadow will appear brighter, and a similar effect may be seen from dew on grass. This partial retro-reflection is created by the refractive properties of the curved droplet's surface and reflective properties at the backside of the droplet.

Some animals' retinas act as retroreflectors see tapetum lucidum for more detail , as this effectively improves the animals' night vision. Since the lenses of their eyes modify reciprocally the paths of the incoming and outgoing light the effect is that the eyes act as a strong retroreflector, sometimes seen at night when walking in wildlands with a flashlight.

A simple retroreflector can be made by placing three ordinary mirrors mutually perpendicular to one another a corner reflector. The image produced is the inverse of one produced by a single mirror. A surface can be made partially retroreflective by depositing a layer of tiny refractive spheres on it or by creating small pyramid like structures. In both cases internal reflection causes the light to be reflected back to where it originated. This is used to make traffic signs and automobile license plates reflect light mostly back in the direction from which it came.

In this application perfect retroreflection is not desired, since the light would then be directed back into the headlights of an oncoming car rather than to the driver's eyes. When light reflects off a mirror , one image appears. Two mirrors placed exactly face to face give the appearance of an infinite number of images along a straight line. The multiple images seen between two mirrors that sit at an angle to each other lie over a circle. A square of four mirrors placed face to face give the appearance of an infinite number of images arranged in a plane.

The multiple images seen between four mirrors assembling a pyramid, in which each pair of mirrors sits an angle to each other, lie over a sphere. If the base of the pyramid is rectangle shaped, the images spread over a section of a torus.

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Note that these are theoretical ideals, requiring perfect alignment of perfectly smooth, perfectly flat perfect reflectors that absorb none of the light. In practice, these situations can only be approached but not achieved because the effects of any surface imperfections in the reflectors propagate and magnify, absorption gradually extinguishes the image, and any observing equipment biological or technological will interfere. In this process which is also known as phase conjugation , light bounces exactly back in the direction from which it came due to a nonlinear optical process.

Not only the direction of the light is reversed, but the actual wavefronts are reversed as well. A conjugate reflector can be used to remove aberrations from a beam by reflecting it and then passing the reflection through the aberrating optics a second time. Materials that reflect neutrons , for example beryllium , are used in nuclear reactors and nuclear weapons. In the physical and biological sciences, the reflection of neutrons off of atoms within a material is commonly used to determine the material's internal structure.

When a longitudinal sound wave strikes a flat surface, sound is reflected in a coherent manner provided that the dimension of the reflective surface is large compared to the wavelength of the sound. As a result, the overall nature of the reflection varies according to the texture and structure of the surface. For example, porous materials will absorb some energy, and rough materials where rough is relative to the wavelength tend to reflect in many directions—to scatter the energy, rather than to reflect it coherently.

This leads into the field of architectural acoustics , because the nature of these reflections is critical to the auditory feel of a space. In the theory of exterior noise mitigation , reflective surface size mildly detracts from the concept of a noise barrier by reflecting some of the sound into the opposite direction.

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