reflections

Examples of reflections in the following topics:

• Reflections

  • Reflections produce a mirror image of a function.  
  • A vertical reflection is a reflection across the $x$-axis, given by the equation:
  • A horizontal reflection is a reflection across the $y$-axis, given by the equation:
  • The third type of reflection is a reflection across a line.  
  • The reflected equation, as reflected across the line $y=x$, would then be:

• The Law of Reflection and Its Consequences

  • The law of reflection states that the angle of reflection equals the angle of incidence.
  • The law of reflection is very simple: The angle of reflection equals the angle of incidence.
  • When we see our reflection in a mirror , it appears that our image is actually behind the mirror -- we see the light coming from a direction determined by the law of reflection.
  • We expect to see reflections off a smooth surface.
  • The law of reflection states that the angle of reflection equals the angle of incidence: θr = θi.

• Polarization By Scattering and Reflecting

  • In the case of polarized sunglasses, for example, when you look through them, reflected light is not entirely filtered out; reflected light can be slightly polarized by the reflection process (as shown in ).
  • The reflected light is more horizontally polarized.
  • Since the light is split into two, and part of it is refracted, the amount of polarization to the reflected light depends on the index of refraction of the reflective surface.
  • where: θb = angle of reflection of complete polarization (also known as Brewster's angle); n1 = index of refraction of medium in which reflected light will travel; and n2 = index of refraction of medium by which light is reflected.
  • Calculate angle of reflection of complete polarization from indices of refraction

• Reflective Thinking

  • Reflective thinking about group work allows students to evaluate both successes and failures of the project and work towards improvement.
  • Reflective thinking is using the scientific method to make a decision.
  • Using reflective thinking in a group setting can allow for intellectual decisions based on defining a problem and using concepts based in logic to select the best solution.
  • Reflective thinking is an excellent tool for identifying positive and negative aspects of a group work experience.
  • In public speaking, John Dewey's methods of reflective thinking are often taught to students.

• Applications: Ultrasound, Sonar, and Medical Imaging

  • Sound waves reflect off different materials differently (when the reflections are collected, they can provide information and images).
  • Controlled reflection of such waves allows images to be received.
  • The use of ultrasound to create images is based on the reflection and transmission of a wave at a boundary.
  • The reflected rays are detected and used to construct an image of the object.
  • Ultrasound waves are sent out then reflected off the objects around the animal.

• Learning to Listen

  • Using active and reflective listening skills can help improve the effectiveness of oral communication.
  • The listener's use of active and reflective listening skills can help improve communication effectiveness.
  • Reflective listening focuses on personal elements of the communication rather than the abstract ideas.
  • Reflective listening should be feeling-oriented and responsive.
  • Verbal response is essential for reflective listening.

• Symmetry of Functions

  • They can have symmetry after a reflection.  
  • The image below shows an example of a function and its symmetry over the $x$-axis (vertical reflection) and over the $y$-axis (horizontal reflection).  
  • The points given, $(1,3)$ and $(-1,-3)$ are reflected across the origin.
  • The graph above has symmetry since the points labeled are reflected over the origin.
  • A function can have symmetry by reflecting its graph horizontally or vertically.  

• Critical reflection

  • Critical reflection attempts to deconstruct the learner's prior assumptions such as beliefs, value systems, attitudes, and social emotion in a rational way.
  • Mezirow points out that learners must engage in critical reflection on their experiences, which could subsequently lead to transformation of meaning perspective.
  • Cranton concisely listed three types of reflection that involves movement toward the emancipatory domain: content, process and premise reflection (Cranton, 1994, p. 48).
  • Content reflection is an examination of the content or description of a problem; process reflection involves checking on the problem; premise reflection happens when the problem itself is questioned.
  • The importance of the premise reflection is repeatedly stressed throughout Mezirow's theory, and he concludes that "premise reflection is the dynamic by which our belief systems - meaning perspective - become transformed (Mezirow, 1991, p. 111)

• Image Reflection by a Plane Mirror

  • A mirror is a reflective surface that bounces off light, thus producing a real or virtual image.
  • The object is the source of the incident rays, and the image is formed by the reflected rays.
  • An image formed by reflection may be real or virtual.
  • The way that we can predict how a reflection will look is by drawing a ray diagram.
  • The angle in which a light ray hits the mirror is the same angle in which it will be reflected back.

• Air Wedge

  • An incident beam of light encounters four boundaries at which the index of refraction of the media changes, causing four reflected beams (or Fresnel reflections) as shown in .
  • The first reflection occurs when the beam enters the first glass plate.
  • The second reflection occurs when the beam exits the first plate and enters the air wedge, and the third reflection occurs when the beam exits the air wedge and enters the second glass plate.
  • The fourth beam is reflected when it encounters the boundary of the second glass plate.
  • The air wedge angle, between the second and third Fresnel reflections, can be adjusted, causing the reflected light beams to constructively and destructively interfere and create a fringe pattern.