Physics: Light and Geometric Optics

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Physics: Light and Geometric Optics by Mind Map: Physics: Light and Geometric Optics

1. The Nature of Light

1.1. Electromagnetic Radiation: Light is part of an energy continuum called electromagnetic radiation. Other examples pf this radiation are: X-rays, Gamma rays, sound waves… All of these together, put in order of the lengths of the wave (wavelength: λ) is called the electromagnetic spectrum.

1.2. Waves:

1.2.1. Crest: Highest point in the wave.

1.2.2. Trough: Lowest point in the wave.

1.2.3. Rest position: No wave.

1.2.4. Wavelength (λ): Distance from the same place in consecutive waves. (E.g. The distance from crest to crest.)

1.2.5. Amplitude: Height or depth of the wave from rest to the crest, or from rest to the trough of the wave.

1.2.6. Frequency: The rate of repetition of the wave.

1.3. Visible light as a wave: We use the similarities between light and the movement of waves to explain several properties of light. The colours of visible light, for instance, can be explained using this wave model. The difference between colours of light is that each colour has a different wave frequency and length.

1.4. Light Duality: Light has properties of waves and particles. Light is often called a photon.

1.5. Which colour bends the most in the prism?

1.5.1. Violet

1.6. Which colour bends the least in the prism?

1.6.1. Red

1.7. What 6 Colours do you see when white light is shone through the prism.

1.7.1. Red, Orange, Yellow, Green, Blue, Violet

1.8. What is the order of the colours?

1.8.1. Red, Orange, Yellow, Green, Blue, Violet

1.9. Where do you think the colours come from?

1.9.1. When white light hits every wall of a prism, it creates arrays of colour.

1.10. In what phenomena in nature do you see the same colour formation?

1.10.1. When sunlight passes through a waterfall.

1.11. Non-luminous Objects: Objects that do not emit their own light . (E.g. Moon)

1.12. Luminous Objects: Objects which produce the light they give off. (E.g. Sun, firefly)

1.13. Chemical Potential Energy: A source which converts chemical energy stored within molecules into light energy. This is often called chemiluminescence. (E.g. Cool lights, living organisms which use chemicals in their bodies can also produce light. This is known as bioluminescence and is a form of chemical energy.

1.14. Heat Energy: A source which converts heat energy within objects burning to produce light. This is called incandescence and it produces a great deal of heat. (E.g. A candle, incandescent lightbulb)

1.15. Electrical Energy: A source which converts electrical energy to light energy. Usually, if you pass electricity through a gas you can get light energy. (E.g. Lightning, neon lights). This can also be associated with heat energy (incandescence), fluorescence, or phosphorescence.

1.16. Nuclear Potential Energy: A source which converts energy stored within the nucleus of atoms into light energy through fission or fusion. (E.g. Atomic bomb)

1.17. Rectilinear Propagation: This is the tendency for light to travel in straight lines especially in a homogenous transparent medium. In general, light travels in straight lines until it strikes something. The properties of that something determines what will happen to the light.

1.17.1. Transparent: Transparent materials transmit light freely - light passes right through it (E.g. glass)

1.17.2. Translucent: Translucent materials transmit some light, absorb and reflect some light. Therefore, you cannot quite see right through it. (E.g. Frosted glass)

1.17.3. Opaque: Opaque materials absorb and reflect all light. (E.g. A blackboard)

1.18. Ray Model of Light: Because light generally travels in straight lines, we often represent these in diagrams by a straight arrow and we call them rays. The arrow points in the direction the light traveling away from its source, and the more rays, the brighter the object appears.

1.19. Getting in Light’s Way: Shadows: Because light travels in straight lines and really cannot bend around objects when an opaque object blocks light travel a shadow is created. The area where light is blocked is called a shadow. The darkest part of the shadow is called an umbra, the light part of a shadow (where some light falls) is called the penumbra.

2. Phenomena of Light 1: Mirrors and Reflection

2.1. Mirrors: A mirror is a non-luminous object with a smooth shiny surface that reflects light in such a way that images form.

2.1.1. Plane Mirror: Any mirror that has a flat reflective surface is called a plane mirror. We use plane mirrors when we look at our reflections for our family purposes. Light bounces off mirrors in a similar way to how a hockey puck bounces off the boards of a ice rink. The reflections in plane mirrors form images that appear to be behind the mirror (about the same distance as the object is from the mirror) but the image looks the same size and shape as the object itself.

2.1.2. Curved Mirrors: Mirrors that are outward-curved (convex mirrors) or inward-curved (concave) surfaces also form images. These images often produce very strange looking images that are different in size the shape than the object, but these mirrors can also be used in many optical devices.

2.2. Light obeys two laws of reflection, and if we use these laws to draw a light ray diagram we can see what images can be formed in planed mirrors.

2.2.1. The incident ray, the normal, and the reflected ray all lie on the same plane.

2.2.2. The angle of the incidence equals the angle of reflection. Therefore, if a light ray struck a mirror at a 45º angle, then it would bounce back at that same angle.

2.2.3. The angles of incidence and reflection are between the normal and the incident and reflective rays respectively.

2.3. Light not only allows us to see objects, some optical devices (light devices - like mirrors, and cameras) allow us to create a likeness of the object. These are called images. (E.g. Overhead projector)

2.4. There are four main characteristics that describe images:

2.4.1. Size: The image can be smaller, larger or the same as the object. Magnification: Magnification is the measure of how much larger or smaller an image is compared with the object itself.

2.4.2. Orientation or Attitude: The image can be upright (the same way up) or inverted (upside-down) in comparison to the object.

2.4.3. Location: In front of the mirror or in the back of the mirror. This can be used to determine the type of image.

2.4.4. Type: The type are location of an image are related. The type of image often depends on its location (for instance, in the mirror, or on a screen). Real Image: The image can be seen on a screen (E.g PowerPoint projector) - the image is in front of the mirror. Virtual Image: The image can only be seen by looking at/through the optical device (E.g. Image from a mirror) - the image is behind the mirror.

2.5. A ray diagram shows how a virtual image forms in a plane mirror. To find the image, rays can be drawn following the laws of reflection, and finding the point where two or more of these light rays cross.

2.6. Characteristics of Images in Plane Mirrors:

2.6.1. Size: The same size as the object

2.6.2. Orientation/Attitude: Upright (the same direction as the object)

2.6.3. Location: The image looks as though it is behind the mirror

2.6.4. Type: Virtual

2.7. An easier way to find and draw images in a plane mirror:

2.7.1. Measure the perpendicular distance from a point on an object to the mirror.

2.7.2. Extend the measurement the same distance from a point on the other side of the mirror. That is where the image of that point appears in the mirror.

2.7.3. Trace the outline from point to point.

2.8. Mirrors which are simply portions of the surface of a polished sphere are used in our daily lives. (E.g. Care side mirrors) When parallel light rays strike a curved surface, each ray of light will reflect at a slightly different position. All of these rays eventually meet at a common point either in front of the mirror, or virtually, behind the mirror.

2.9. Focal Point: The point on the axis of a lens or mirror to which parallel rays of light converge or from which they appear to diverge after refraction or reflection

2.10. Vertex: The point at which the sides of an angle intersect.

2.11. Focal Length: the distance between the centre of a convex lens or a concave mirror and the focal point of the lens or mirror - the point where parallel rays of light meet, or converge.

2.12. Real Image: The original image found on the plane.

2.13. A concave mirror, or converging mirror, has a surface that curves inward like a bowl. *CONCAVE - a cave that you go inside*

2.14. A convex mirror or diverging mirror has a surface that curves outward. Instead of “collecting” light rays at a point, a diverging mirror spreads out the rays.

2.15. Magnification is the measure of how much larger or smaller an image is compared with the object itself. The image can be larger, smaller or the same size as the object. The magnification can be calculated using the ratio of the height of image to the height of the object or the ratio of the distance from the image to the mirror and distance from the object to the mirror. Knowing the magnification can be useful when trying to figure out how much an optical device may magnify an object.

2.16. Calculating Magnification:

2.16.1. Magnification = image height/object height M=hi/ho

2.16.2. Magnification = image distance/ object distance M=di/do

2.17. If the image is larger than an object it will have a magnification >1 (more than 1). If the image is equal in size to the object it will have a magnification equal to 1. What is the magnification of an image that is smaller than an object? <1 (less than 1).

2.18. Drawing a Concave Mirror Ray Diagram

2.18.1. The first ray of a concave mirror ray diagram travels from a point on the object parallel to the principal axis. Any ray that is parallel to the principal axis will reflect through the the focal point on a converging mirror.

2.18.2. The second ray travels from a point on the object toward the focal point. Any ray that passes through the focal point on a converging mirror will be reflected back parallel to the principal axis.

2.18.3. Draw the real image where the rays intersect.

2.19. Drawing a Convex Mirror Ray Diagram

2.19.1. The first ray of a convex mirror ray diagram travels from a point on the object parallel to the principal axis. Any ray that is parallel to the principal axis will appear to have originated from the focal point on a diverging mirror.

2.19.2. The second ray travels from a point on the object toward the focal point. Any ray that is directed at the focal point on a diverging mirror will be reflected back parallel to the principal; axis.

2.19.3. Draw the virtual image where the rays appear to intersect.

3. Phenomena of Light 2: Lenses and Refraction

3.1. Light rays can be absorbed (in opaque or dark objects)

3.2. Reflected from (shiny or translucent objects)

3.3. Transmitted (in transparent objects)

3.4. When light is transmitted from one transparent medium (such as air) to another transparent medium (such as water) light changes direction or bends.

3.5. (Outcome: It looks like the spoon is broken)

3.6. The change in direction is when light travels between mediums and is known as refraction, this occurs because light is changing speed when it changes mediums.

3.7. Light can either bend away from the normal or toward the normal. When light is slowing down (or going from a less dense medium, like air to a denser medium like glass) light will bend towards the normal.

3.7.1. \

3.8. Optical Density: The term used to describe the relative speed of light in a given medium is “optical density”. As the optical density increases, the velocity of light in that medium decreases.

3.9. The Index of Refraction: The amount by which a transparent medium decreases the speed of light is called the index of refraction (or n). The more optically dense the medium, the more it will slow the speed of light and the larger its refractive index or index of refraction.

3.10. Calculating the Index of Refraction and Speeds of Light in Various Media: To calculate the index of refraction, we need to compare the speed (v- for velocity) of light in air with the speed of light in the other media.

3.11. Predicting Angles of Refraction - Snell’s LawThe indices of refraction are useful in predicting how much the light will slow down and therefore, the angle that the light will bend. This can be useful for designing optical devices such as eyeglasses and cameras which use lenses . There is a formula that scientists and engineers use in order to calculate the new angle that a ray will take as a beam of light strikes the interface between two media.

3.12. n1sinø1 = n2sinø2 Where n = the indices of refraction for the different media, and ø1 is the angle of incidence for the one medium and ø2 is the angle of refraction in the second medium. This is known as Snell’s Law.

3.13. When a light ray travelling from a more optically dense material to less dense material enters at a large angle, the ray bends away from the normal so much that the light does not actually escape the first medium. This means that the angle of refraction is greater than 90º, and we call this phenomenon - total internal reflection. The light is being reflected back into the dense material.

3.14. The "critical angle" - At a certain incident angle, called the critical angle, the refracted angle is exactly 90 and therefore follows a path along the surface of the media boundary. Even though the light refracts, it does not leave the first medium and is "trapped".

3.15. If the angle of incidence is increased beyond the critical angle, the angle is then totally reflected back. This phenomenon is used in a variety of optical devices and most importantly in fibre optic devices which carries your internet signal to you house.

3.16. Calculating the Index of Refraction and Speeds of Light in various media:

3.16.1. n=Va/Vg=c/v

3.17. Principle Axis: An imaginary line drawn through the optical centre of a lens.

3.18. Axis of Symmetry: An imaginary vertical line drawn through the optical centre of a lens.

3.19. Principle Focus: The focal point where the light either comes to a focus or appears to diverge from a focus is given the symbol F, while that in the opposite side of the lens is represented by F'.

3.20. Focal Length: The distance from the axis of symmetry to the principal focus measured along the principal axis,

3.21. Optical Centre: The centre of the lens.