grade 10-physics_fetena_net_1b5e

Mirrors and Lenses

Laws of Reflection and Refraction

• Apply the laws of reflection and refraction.
• Describe image formation as a consequence of reflection and refraction.
• Perform calculations based on the law of reflection and refraction.
• Distinguish between real and virtual images.

Mirror

• A mirror is a reflective surface that does not allow the passage of light and instead bounces it off, thus producing an image.
• Two types of mirrors: plane and spherical.

Plane Mirrors

• A mirror that has a flat reflective surface is called a plane mirror.
• Object: The actual, physical candle.
• Image: The picture you see in the mirror.
• The object is the source of the incident rays and the image is formed by the reflected rays.

Image Formation by a Plane Mirror

• To locate the image of an object we need to find the position where at least two rays intersect after reflecting off the mirror.
• Virtual Image: The reflected rays diverge, and the image is found by extending the reflected rays back to find the point where they appear to come from.
• The virtual image appears to be behind the mirror at the same distance as the object is in front of the mirror, is upright and of the same size, but is laterally inverted.

Key Concepts for Plane Mirrors

• The image formed by a plane mirror is:
  • Virtual.
  • The same distance behind the mirror as the object is in front of the mirror.
  • Laterally inverted (inverted from side to side).
  • The same size as the object.
  • Upright.

Number of Images Formed by Two Plane Mirrors Inclined to Each Other

• If two plane mirrors are inclined to each other at an angle \theta, the number of images formed is:
  • \approx (\frac{360^o}{\theta} - 1), if \frac{360^o}{\theta} is an even integer.
  • \approx \frac{360^o}{\theta}, if \frac{360^o}{\theta} is an odd integer.
• For example, 5 images are formed by two mirrors at a 60° angle.
• For any value of \theta between 90° and 120°, the number of maximum images formed is n = 3.
  • If \theta is given, n is unique, but if n is given, \theta is not unique.
• The number of images seen may be different from the number of images formed and depends on the position of the observer relative to the object and mirrors.
  • For instance, if \theta = 120^o, the maximum number of images formed will be 3, but the number of images seen may be 1, 2 or 3 depending on the position of the observer.

Uses of Plane Mirrors

• In looking glasses
• In construction of kaleidoscope, telescope, sextant, and periscope
• For seeing round the corners
• As deflector of light

Spherical Mirrors

• A spherical mirror is formed by the inside (concave) or outside (convex) surfaces of a sphere.
  • Concave mirror: surface curved inward (converge incoming parallel rays).
  • Convex mirror: surface that curves outward (diverge light).

Important Terms for Spherical Mirrors

• Center of Curvature (C): The center of the sphere of which the mirror is a part.
• Radius of Curvature (R): The radius of this sphere.
• Pole (P): The middle point of the reflecting surface of the mirror.
• Principal Axis: The straight line passing through the center of curvature and the pole.
• Aperture: The circular outline of the mirror (measure of the size of the mirror).
• Principal Focus (F): The common point where a beam of light incident on a spherical mirror parallel to the principal axis converges to or appears to diverge from after reflection.
• Focal Length (f): The distance between the pole and the principal focus of the mirror.
• For mirrors of small apertures, the radius of curvature is equal to twice the focal length, which is expressed as: R = 2f. This implies that the principal focus of a spherical mirror lies midway between the pole and center of curvature.

Ray Diagrams for Spherical Mirrors

• Locate the image of an object by considering any two of the following rays:
  1. Ray striking the pole: A ray of light striking the pole of the mirror at an angle is reflected back at the same angle on the other side of the principal axis.
  2. Parallel ray:
     • Concave mirror: the ray parallel to the principal axis is reflected through the principal focus.
     • Convex mirror: the parallel ray appears to come from the principal focus.
  3. Ray through center of curvature: A ray passing through the center of curvature hits the mirror along the direction of the normal to the mirror at that point and retraces its path after reflection.
  4. Ray through focus: A ray of light heading towards the focus or incident on the mirror after passing through the focus returns parallel to the principal axis.
• In all cases, the laws of reflection are followed (angle of incidence equals the angle of reflection).

Image Formation by a Concave Mirror

• The intersection of at least two reflected rays gives the position of the image of the object.

Image Formation by a Concave Mirror for Different Positions of the object

• The properties of the image depend on the location of the object.

Table 6.2 Image formation by a concave mirror for different positions of the object

Uses of Concave Mirrors

• In torches, search-lights and vehicle headlights to get powerful parallel beams of light.
• As shaving mirrors to see a larger image of the face.
• Dentists use concave mirrors to see large images of the teeth of their patients.
• Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

Image Formation by a Convex Mirror

Table 6.3 Nature, position and relative size of the image formed by a convex mirror

Uses of Convex Mirrors

• Commonly used as rear-view (wing) mirrors in vehicles.
• They give an erect, though diminished, image, and have a wider field of view.

Mirror Formula and Magnification

• Object distance (u): The distance of the object from the pole of the mirror.
• Image distance (v): The distance of the image from the pole of the mirror.
• Focal length (f ): The distance of the principal focus from the pole.
• Mirror Formula: \frac{1}{v} + \frac{1}{u} = \frac{1}{f}
• Magnification (m): The relative extent to which the image of an object is magnified with respect to the object’s size.
  • m = \frac{\text{height of the image (h')}}{\text{height of the object (h)}} = \frac{h'}{h}
  • m = \frac{h'}{h} = - \frac{v}{u}
• These formulas are valid for spherical mirrors in all positions of the object.
• Use the sign convention from Table 6.4 when substituting numerical values to solve the mirror formula problems.

Table 6.4 Sign conventions for spherical mirrors

Example 6.5

• A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.

• Given: radius of curvature, R = -3.00 m and object distance, u = +5.00 m

• Focal length: f = \frac{R}{2} = \frac{-3.00}{2} = -1.50 m

• Using the mirror equation,

  • \frac{1}{v} + \frac{1}{u} = \frac{1}{f}
  • \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-1.50} - \frac{1}{+5.00}
  • \frac{1}{v} = \frac{-5.00 - 1.50}{7.50}
  • v = \frac{-7.50}{6.50} = -1.15 m

• Therefore, the image is 1.15 m at the back of the mirror.

• Magnification:

  • m = \frac{h'}{h} = -\frac{v}{u} = -\frac{-1.15 m}{5.00 m} = +0.23

• The image is thus virtual, erect and smaller in size by a factor of 0.23.

Example 6.6

• An object, 6.0 cm in size, is placed at 25.0 cm in front of a concave mirror of 15.0 cm focal length. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Determine the nature and the size of the image.

• Given: object size, h = +6.0 cm, object distance, u = +25.0 cm and focal length, and f = +15.0 cm.

• Using the mirror equation,

  • \frac{1}{v} + \frac{1}{u} = \frac{1}{f}
  • \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15.0} - \frac{1}{25.0} = \frac{5.00 - 3.00}{75}
  • v = 37.5 m

• The screen should be placed at 37.5 cm in front of the mirror. The image is real.

• Magnification:

  • m = \frac{h'}{h} = - \frac{v}{u}
  • h' = -\frac{hv}{u} = \frac{-(37.5 cm)(6.0 cm)}{(25.0 cm)} = -6.0 cm

• Thus, the height of the image is - 6.0 cm. The negative sign implies that the image is inverted and enlarged.

Lenses

• A lens is a curved piece of transparent material that is smooth and regularly shaped so that when light strikes it, the light refracts in a predictable and useful way.
• A transparent material bound by two surfaces of which one or both are spherical forms a lens.

Types of Lenses

• Convex Lens: thicker at the middle (converging lenses).
• Concave Lens: thicker in the edges than at the middle (diverging lenses).
• Key Concept: Concave lenses cause light to diverge, and convex lenses cause light to converge.
• A lens has two spherical surfaces - the centers of these spheres are called the centers of curvature (C) of the lens (C1 and C2).
• Principal Axis: An imaginary straight line passing through the two centers of curvature of a lens.
• Optical Center (O): The central point of a lens - A ray of light through the optical center of a lens passes without suffering any deviation.
• Aperture: The effective diameter of the circular outline of a spherical lens.
• Principal Focus: Focus on the principal axis.
  • Convex lens - point where rays converge.
  • Concave lens - point from which rays appear to diverge.
• A lens has two principal foci on opposite sides, represented by F1 and F2.
• Focal Length (f ): The distance of the principal focus from the optical center of a lens.

Ray Diagrams for Lenses

• For drawing ray diagrams in lenses, consider any two of the following rays:
  1. A ray of light from the object, parallel to the principal axis:
     • Convex Lens: after refraction, passes through the principal focus on the other side of the lens.
     • Concave Lens: the ray appears to diverge from the principal focus located on the same side of the lens.
  2. A ray of light passing through a principal focus:
     • Convex Lens: after refraction, will emerge parallel to the principal axis.
     • Concave Lens: A ray of light appearing to meet at the principal focus, after refraction, will emerge parallel to the principal axis.
  3. A ray of light passing through the optical center of a lens will emerge without any deviation.

Image Formation by Convex Lenses

• The nature, position, and relative size of the image depend on the location of the object.

Table 6.5 Nature, position and relative size of the image formed by a convex lens for various positions of the object

Image Formation by Concave Lenses

• A concave lens will always give a virtual, erect, and diminished image, irrespective of the position of the object.

Table 6.6 Nature, position, and relative size of the image formed by a concave lens for various positions of the object

Lens Formula and Magnification

• Lens Formula: \frac{1}{u} + \frac{1}{v} = \frac{1}{f}
• Magnification:
  • m = \frac{h'}{h}
  • m = \frac{h'}{h} = -\frac{v}{u}
• The above lens and magnification formula are general and applicable to any spherical lens in any situations.
• Use the sign conventions in table 6.7 when substituting numerical values for solving problems relating to lenses.

Table 6.7 Sign conventions for lenses

Example 6.7

• A concave lens has a focal length of 15 cm. At what distance from the lens should the object be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens.
• Given: image distance v = -10 cm and focal length f = -15 cm.
• Lens formula:
  • \frac{1}{v} + \frac{1}{u} = \frac{1}{f}
  • \frac{1}{u} = \frac{1}{f} - \frac{1}{v} = \frac{1}{-15.0} - \frac{1}{-10.0} = \frac{-2+3}{30} = \frac{1}{30}
  • v = 30 cm
• Thus, the object distance is 30 cm.
• Magnification:
  • m = -\frac{v}{u} = - \frac{-10}{30} = +0.33
• The positive sign shows that the image is erect and virtual. The image is one-third the size of the object.

Example 6.8

• A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of 10 cm focal length. The distance of the object from the lens is 15 cm. Find the nature, position, and size of the image. Also find its magnification.

• Given height of the object, h = +2.0 cm, focal length, f = +10 cm and object distance, and u = +15 cm.

• Using the lens formula:

  • \frac{1}{v} + \frac{1}{u} = \frac{1}{f}
  • \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{10} - \frac{1}{15} = \frac{3-2}{30}
  • v = +30cm

• The positive sign of v shows that the image is formed at a distance of 30 cm on the other side of the optical center. The image is real and inverted.

• Magnification:

  • m = \frac{h'}{h} = - \frac{v}{u}
  • h' = -\frac{hv}{u} = \frac{-(2)(30)}{(15)} = -6.0cm

• Magnification:

  • m = - \frac{v}{u} = \frac{+30}{+15} = -2

• The negative signs of m and h’ show that the image formed is inverted and real. It is formed below the principal axis. Thus, a real, inverted image, 4 cm tall is formed at a distance of 30 cm on the other side of the lens. The image is two times enlarged.

Section Summary

• The image formed by a plane mirror is virtual, erect and of the same size as that of the object such that the object and its image appear to be equidistant from the mirror.
• A convex mirror is a diverging mirror in which the reflective surface bulges towards the light source. The image formed by convex mirrors is smaller than the object but gets larger as they approach the mirror.
• A concave mirror has a reflective surface that is curved inward and away from the light source. The image formed by a concave mirror shows different image types depending on the distance between the object and the mirror.
• The lens which is thick in the middle and thin at the edges is called a convex lens whereas the lens which is thin in the middle and thick at the edges is called a concave lens.
• Convex lens is also known as a converging lens as it converges the parallel rays of light at a point after refraction.
• Concave lens is also known as diverging lens as it diverges the parallel beam of light after refraction.
• The type of image formed by a convex lens depends on the position of the object that can be placed at different positions in front of the lens. However, a concave lens always produces a virtual, erect and diminished images.
• The mirror as well as lens equation expresses the quantitative relationship between the object distance, the image distance and the focal length.

The Human Eye and Optical Instruments

The Human Eye

• The human eye is like a camera, where its lens system forms an image on a light-sensitive screen called the retina.
• Light enters the eye through the cornea, a thin membrane that forms the transparent bulge on the front surface of the eyeball.
• The eyeball is approximately spherical in shape with a diameter of about 2.3 cm.
• Most of the refraction of light rays entering the eye occurs at the outer surface of the cornea. The crystalline lens merely provides the finer adjustment of the focal length required to focus objects at different distances on the retina.
• Behind the cornea, you find the iris, which is a dark muscular diaphragm that controls the size of the pupil.
• The pupil regulates and controls the amount of light entering the eye.
• The eye lens forms an inverted real image of the object on the retina.
• The retina is a delicate membrane with an enormous number of light-sensitive cells.
• The light-sensitive cells get activated upon illumination and generate electrical signals that are sent to the brain via the optic nerves.
• The brain interprets these signals and processes the information so that you perceive objects as they are.
• Key Concept: The human eye consists of a lens system that focuses images on the retina, where the optic nerve transfers the messages to the brain.

Power of Accommodation

• The ciliary muscles can modify the curvature of the eye lens and thus change its focal length.
• When the muscles are relaxed, the lens becomes thin, and its focal length increases, enabling us to see distant objects clearly.
• When looking at objects closer to the eye, the ciliary muscles contract, increasing the curvature of the eye lens.
• The focal length of the eye’s lens cannot be decreased below a certain minimum limit.
• The ability of the eye’s lens to adjust its focal length is called accommodation.

Near Point and Far Point

• The minimum distance at which objects can be seen most clearly without strain is called the least distance of distinct vision (near point of the eye).
• For a young adult with normal vision, the near point is about 25 cm.
• The farthest point up to which the eye can see objects clearly is called the far point of the eye. It is infinity for a normal eye.
• A normal eye can see objects clearly that are between 25 cm and infinity.

Defects of Vision and Their Correction

• Sometimes, the eye gradually loses its power of accommodation - the person cannot see the objects distinctly and comfortably. The vision becomes blurred due to the refractive defects of the eye.

Myopia (Near-Sightedness)

• A person with myopia can see nearby objects clearly but cannot see distant objects distinctly.
• The far point is nearer than infinity.
• The image of a distant object is formed in front of the retina.
• This defect may arise due to excessive curvature of the eye lens or elongation of the eyeball.
• This defect can be corrected by using a concave lens of suitable power.

Hypermetropia (Far-Sightedness)

• A person with hypermetropia can see distant objects clearly but cannot see nearby objects distinctly.
• The near point is farther away from the normal near point (25 cm) - such a person has to keep reading material much beyond 25 cm from the eye for comfortable reading.
• The light rays from a close by object are focused at a point behind the retina.
• This defect arises either because the focal length of the eye lens is too long, or the eyeball has become too small.
• This defect can be corrected by using a convex lens of appropriate power.
  Eye glasses with converging lenses provide the additional focusing power required for forming the image on the retina.

Presbyopia

• The power in accommodation of the eye usually decreases with age, and the near point gradually recedes.
• Without corrective eye-glasses, they have difficulty seeing nearby objects comfortably and clearly. This defect is called presbyopia.
• It arises due to the gradual weakening of the ciliary muscles and diminishing flexibility of the eye lens.
• A person may suffer from both myopia and hypermetropia and require bi-focal lenses.
  • The upper portion consists of a concave lens for distant vision.
  • The lower part is a convex lens for near vision.

Optical Instruments

• A number of optical devices and instruments have been designed utilizing the reflecting and refracting properties of mirrors and lenses. Examples include: periscope, kaleidoscope, binoculars, camera, telescopes, and microscopes.

Simple Microscope (Magnifier)

• A converging lens of small focal length.
• The lens is held near the object (one focal length away or less), and the eye is positioned close to the lens on the other side.
• Erect, magnified and virtual image of the object at a distance can be viewed comfortably (at 25 cm or more).
• Key Concept: The image formed by a magnifying glass is erect, magnified and virtual.

Compound Microscope

• For much larger magnifications, two lenses are used (one compounding the effect of the other).
• A compound microscope has more than one objective lens, each providing a different magnification.
• An object is placed close to a convex lens called the objective lens.
• This lens produces an enlarged image inside the microscope tube.
• The light rays from that image then pass through a second convex lens called the eyepiece lens.
• This lens further magnifies the image formed by the objective lens.

Telescopes

• Used to examine objects that are very far away.

Refracting Telescope

• Uses a combination of lenses to form an image.
• Simplest refracting telescopes use two convex lenses to form an image of a distant object.
• An objective and an eyepiece (like the compound microscope).
• Objective forms a real, inverted image of a distant object very near the focal point of the eyepiece.
• The main purpose of a telescope is to gather as much light as possible from distant objects using a large objective lens.
• This makes images of far away objects look brighter and more detailed when they are magnified by the eyepiece. With a large enough objective lens, it is possible to see stars and galaxies that are many trillions of kilometers away.

Reflecting Telescope

• Can be made much larger than refracting telescopes.

• Reflecting telescopes have a concave mirror instead of a concave objective lens to gather the light from distant objects.

• The large concave mirror focuses light onto a secondary mirror that directs it to the eyepiece, which magnifies the image.

• Because only the one reflecting surface on the mirror needs to be made carefully and kept clean, telescope mirrors are less expensive to make and maintain than lenses of a similar size. Also, mirrors can be supported not only at their edges but also on their backsides. They can be made much larger without sagging under their own weight.

• Key Concept: Light entering the telescope tube is reflected by a concave mirror onto the secondary mirror. An eyepiece is used to magnify the image formed by the concave mirror.

Section Summary

• The simple defects of vision (long and short sight) are attributed to the inability of the eye lens to focus images of near and far objects on the retina - Simple lenses enable these defects to be corrected.
• The function of optical instruments is to extend the performance of the human eye in a variety of ways.
• The magnifying glass creates an enlarged, erect and virtual image of an object placed closer to the lens than the focal point.
• The compound microscope is an instrument for looking at very small objects by using an objective to produce an enlarged real intermediate image which is then further enlarged by an eyepiece used as a magnifying glass.
• The telescope is an instrument for looking at distant objects: the refracting telescope uses a large objective lens and an eyepiece lens to form an image of a distant object. The reflecting telescope uses a large concave mirror that gathers light and an eyepiece lens to form an image of a distant object.

Primary Colors of Light and Human Vision

Light Receptors in the Eye

• Light travels into the eye to the retina, located on the back of the eye. The retina is covered with millions of light receptive cells called cones (which are sensitive to color) and rods (which are more sensitive to intensity).
• When these cells detect light, they send signals to the brain.
  All of these cells, working in combination with connecting nerve cells, give the brain enough information to interpret and name colors.
• **Key Concept: Light receptors within the eye transmit messages to the brain which produces the familiar sensations of color.
• Different wavelengths of light are perceived as different colors.

Cone Sensitivity

• You are able to perceive all colors because there are three sets of cones in your eyes: one set that is most sensitive to red light, another that is most sensitive to green light, and a third that is most sensitive to blue light.

Primary Colors

• Key Concept: Red, green and blue are the primary colors. All other colors of the visible light spectrum can be produced by properly adding different combinations of these three colors.
• Adding equal amounts of red, green, and blue light produces white light.

Section Summary

• Red, green and blue are the primary colors of light.
• Rods and cones are the two major types of light-sensing cells (photoreceptors) in the retina.

Color Addition of Light

Additive Color System

• The additive color system reproduces colors by adding the primary colors of light: red, green, and blue. All the colors that can be produced by a three-color additive system are combinations of these three primary colors.
• Mixing the additive color primaries of red, green, and blue give the range of colors that you see. So red, green and blue are therefore called the additive primary colors.

Secondary Colors of Light

• The result of adding two primary colors of light is easily seen by viewing the overlap of the two or more circles of primary light.
• In the areas where two primary colors overlap, a secondary color appears.
• Green and blue create cyan.
• Blue and red produce magenta.
• Red and green produce yellow.
• Red + Green = Yellow
• Red + Blue = Magenta
• Blue + Green = Cyan Yellow, magenta and cyan are sometimes referred to as secondary colors of light since they can be produced by the addition of equal intensities of two primary colors of light.
  When added in equal proportions, red, green, and blue result in white light. The absence of all three colors results in black.
• Key Concept Combinations of two of the primary colors follow the rules of additive color mixing so as to produce the secondary colors of light: cyan, magenta, and yellow.
• The addition of these three primary colors of light with varying degrees of intensity will result in the countless other colors that you are familiar with. So, all the other colors can be produced by different combinations of red, green and blue.

Applications of Color Addition

• Color television, color computer monitors and on-stage lighting at the theaters. A digital projector also works using the additive systems.
  *
  Each of these applications involves the mixing or addition of colors of light to produce a desired appearance.

Section Summary

• The combination of the three primary colors of light with equal proportions produce white light.
• All the other colors of light can be produced by different combinations of red, green and blue.

Color Subtraction of Light Using Filters

Color Subtraction

• The colors that are absorbed are ’subtracted’ from the reflected light that is seen by the eye.
• A black objects absorbs all colors where as a white object reflects all colors.
• A blue objects reflects blue and absorbs all other colors. The primary and secondary colors of light for the substractive colors are opposite to the colors addition.
• Illustrations of color subtraction:
  • Cyan - Blue = (Green + Blue) - Blue = Green
  • Yellow - Green = (Red + Green) - Green = Red
  • Magneta - Red = (Red + Blue) - Red = Blue Yellow, magenta and cyan are considered as the subtractive primary colors while red, green and blue are the secondary subtractive colors.
    On the other hand, the complimentary colors are the colors that are absorbed by the subtractive primaries. Cyan’s complement is red; magenta’s complement is green; and yellow’s compliment is blue.
• Pigments are substances which give an object its color by absorbing certain frequencies of light and reflecting other frequencies. For example, a red pigment absorbs all colors of light except red which it reflects. Paints and inks contain pigments which give the paints and inks different colors.
  A filter is also defined as a substance or device that prevents certain things from passing through it while allowing certain other things to pass.
• Color filters allow only certain colors of light to pass through them by absorbing all the rest. When white light shines on a red filter, for example, the orange, yellow, green, blue, and violet components of the light are absorbed by the filter allowing only the red component of the light to pass through to the other side of the filter.

Color Subtraction of Light Using Filters or Pigments

• Yellow