UNIVERSITY OF GUYANA FACULTY OF NATURAL SCIENCES DEPART. OF MATH, PHYS & STATS PHY 110 – PHYSICS FOR ENGINEERS LECTURE 9 (THURSDAY, NOVEMBER 3, 2011) 1

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 2

2.7 Plane Mirrors. Image Location 3 Image Formation by Plane Surfaces: Physics for the IB Diploma by Tim Kirk, pg 160.

2.7 Plane Mirrors. Image Location 4 Image Formation by Plane Surfaces: Consider the situation: 1. Lights sets off in all direction from every part of the body. 2. Each ray is reflected based on the laws of reflection. 3. These rays enter the eye of the observer. 4. The location of the image seen by the observer arises because the rays are assumed to have travelled in straight lines. Physics for the IB Diploma by Tim Kirk, pg 160.

2.7 Plane Mirrors. Image Location 5 Properties of the Image: 1. Upright 2. Same size as object. 3. Virtual. 4. Image distance is Object distance. 5. Laterally inverted. Physics for the IB Diploma by Tim Kirk, pg 160.

2.8 Magnification 6 Magnification m: This is the ratio of image distance to the object distance or height of the image to the height of the object. Where u, and v represent object and image distances.

2.9 Applications of Plane Mirrors 7 Home Work: How are plane mirrors utilised in: 1. Corner reflectors. 2. Optical levers. 3. Sextants.

2.10 Spherical Mirrors 8 Introduction: Mirror, optical device, commonly made of glass, with a smooth, polished surface that forms images by the reflection of rays of light. Mirrors made of brass are mentioned in the Bible, and mirrors of bronze were in common use among the ancient Egyptians, Greeks, and Romans. Polished silver was also used by the Greeks and Romans to produce reflections. Crude forms of glass mirrors were first made in Venice in 1300.

2.10 Spherical Mirrors –Types, Cardinal Pts. 9 Introduction Cont’d: By the end of the 17th century mirrors were made in Britain and the manufacture of mirrors developed subsequently into an important industry in the other European countries and in the United States. In addition to their general household use, mirrors are used in scientific apparatus, for example, as important components in microscopes and telescopes. Microsoft ® Encarta ® 2007.

2.10 Spherical Mirrors 10 Types: Curved mirrors are of two types namely: 1. Concave: Light is reflected on the inside of the curvature. 2. Convex: Reflection occurs on the outside of its curvature.

2.10 Spherical Mirrors - Types 11 Concave Mirror: curves inward like the inside surface of a hollow sphere. Light striking the surface of a concave mirror reflects inward, or converges. The size, position, and type of image— real or virtual—depends on the size and position of the object and the focal point of the mirror, or the place where light rays converge. In the following illustration, an object is placed between a concave mirror and its focal point. The mirror forms a larger, upright, virtual image. Microsoft ® Encarta ® 2007.

2.10 Spherical Mirrors - Types 12

2.10 Spherical Mirrors - Types 13 Convex Mirror: curves outward like the outer surface of a ball. Light striking the surface of a convex mirror reflects outward, or diverges. In this illustration, parallel light rays from an object that strike the mirror are reflected as though they came from an image behind the mirror. These light rays form an upright, smaller, virtual image; that is, the brain perceives the diverging rays as though they came from an image behind the mirror. Microsoft ® Encarta ® 2007.

2.10 Spherical Mirrors - Types 14

2.10 Spherical Mirrors – Cardinal Points 15 Cardinal points of Curved Mirrors: 1. Aperture AB: Curvature of the mirror. 2. Pole of Mirror P: Mid-point of aperture AB. 3. Centre of Curvature C: Centre of the sphere of which the mirror is a part. 4. Principal Axis: Imaginary line connecting pole of mirror P to the centre of curvature C. 5. Focal point F: Point on the principal axis where a parallel beam converges or appears to diverge after reflection.

2.10 Spherical Mirrors – Cardinal Points 16 Cardinal points of Curved Mirrors Cont’d: 1. Focal length f: Distance between pole P and focal point F. 2. Radius of Curvature r: Radius of the sphere of which the mirror is a part. Distance between pole P and centre of curvature C.

2.10 Spherical Mirrors – Cardinal Points 17 Cardinal points of Curved Mirrors Cont’d: Physics by Douglas Giancoli, 4 th Ed., pp 651, 656

2.11 Reflection on Curved Surfaces, Images. 18 Comparing the Concave and Convex Mirrors:

2.11 Reflection on Curved Surfaces, Images 19 The nature and location of images produced by both mirrors depends on the location of the object with respect to the mirrors. Generally, images that are produced may be real or virtual, magnified or diminished, upright or inverted.

2.12 Ray Diagram Construction 20 Image Formation in Curved Mirrors: Information as the nature and size of images produced by curved mirrors may be deduced from ray diagram construction or by calculation using the mirror formula. For ray diagram construction, two of the following three rays drawn from the top of the object must intersect to produce the image:

2.12 Ray Diagram Construction 21 Image Formation in Curved Mirrors Cont’d: 1. Ray 1: Travels parallel to the principal axis and after reflection passes through the focal point or appears diverge from it. 2. Ray 2: This is a reverse of Ray 1. It passes through the focal point and after reflection travels parallel to the principal axis. 3. Ray 3: It passes through the centre of curvature and strikes the mirror normally and is reflected back on itself.

2.12 Ray Diagram Construction 22 Image Formation in a Concave Mirror: Physics by Douglas Giancoli, 4 th Ed., pp 655-6

2.12 Ray Diagram Construction 23 Image Formation in Convex Mirror: Physics by Douglas Giancoli, 4 th Ed., pp 655-6

2.12 Ray Diagram Construction 24 Comparison of Images: Physics by Douglas Giancoli, 4 th Ed., pp 655-6

2.12 Ray Diagram Construction 25 Concave Mirror 1. Upright 2. Magnified 3. Virtual. 4. Located behind mirror. Convex Mirror 1. Always Upright 2. Always Diminished 3. Always Virtual. 4. Always Located behind the mirror between pole and focus. Properties of Image produced by:

2.12 Ray Diagram Construction 26 Home Work: Determine the location and properties of the image produced by a concave mirror when the object is: 1. At F. 2. Between F and C. 3. At C. 4. Beyond C.

2.13 Mirror Formula 27 Mirror Formula: Information as to the nature and location of images formed by curved mirrors may be obtained from calculation employing the mirror formula used in conjunction with the Real-is- Positive sign convection. Where u, v, f and r represent object distance, image distance, focal length and radius of curvature.

2.13 Mirror Formula 28 Real-is-Positive Sign Convention: This convention states that a distance measured to a real object or image is deemed a positive distance conversely a distance measured to a virtual object or image is a negative distance. NB: The focal length of a concave mirror is deemed positive given that its focal point is real while for the convex mirror it is negative since its focal point is virtual.

Lecture Notes: For this information, visit my website: In the event of any other issues to be resolved, 29

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