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Chapter 5: Light and Vision CHAPTER 5: LIGHT AND VISION ╞╡§¥ Physics SPM 2015 These notes have been compiled in a way to make it easier for revision. The topics are not in order as per the syllabus. 5.1 Mirrors and Lenses 5.1.1 Image Characteristics Image characteristics are described using the following three categories: Same Image is exactly the same size as the object Size Magnified Image appears bigger than the object Diminished Image appears smaller than the object Image appears to be in the same direction as the object Direction Upright Inverted Image appears upside down compared to object Real Real images are images you can capture on a screen. Type Mirrors: Images are formed on the same side of the mirror as the object Lenses: Images are formed on the opposite side of the lens from the object Virtual Virtual images are images you can see but cannot capture on a screen. Mirrors: Images are formed on the opposite side of the mirror from the object Lenses: Images are formed on the same side of the lens as the object 5.1.2 Plane mirrors i Incident ray r normal Reflected ray Law of light reflection: • The reflected angle is always the same as the incident angle. • The incident ray, reflected ray, and normal line are in the same plane. Characteristics of an image formed by a plane mirror: Size Same Direction Upright, laterally inverted Type Virtual Distance Distance of an image from the plane mirror is the same as the distance of the object from the mirror Hoo Sze Yen www.physicsrox.com Page 1 of 8 ╞╡§¥ Physics Chapter 5: Light and Vision SPM 2015 5.1.3 Curved Mirrors vs Lenses Concave mirror Also known as Focal lengths Converging mirrors Positive E.g. f = +20cm. Convex mirror Diverging mirror Negative E.g. f = -20cm. For both concave and convex mirrors, the focal length is half the radius; i.e. CF = FP. Convex lens Also known as Focal lengths Concave lens Converging lens Positive E.g. f = +20cm. Diverging lens Negative E.g. f = -20cm. Determining the Position and Characteristics of an Image with a Ray Diagram Concave mirror A ray parallel to the principal axis is reflected to pass through F A ray through F is reflected parallel to the principal axis Convex mirror A ray through C is reflected back along its own path A ray parallel to the principal axis is reflected as if it came from F A ray towards F is reflected parallel to the principal axis A ray towards C is reflected back along its own path Hoo Sze Yen www.physicsrox.com Page 2 of 8 ╞╡§¥ Physics Chapter 5: Light and Vision SPM 2015 Convex lens A ray parallel to the principal axis is refracted to pass through F A ray through F is refracted parallel to the principal axis Concave lens A ray through C travels straight along its own path A ray parallel to the principal axis is refracted as if it came from F A ray towards F is refracted parallel to the principal axis A ray towards C travels straight along its own path To determine the position and characteristics of an image using a ray diagram: 1. Draw two rays emanating from the top of the object to the mirror or lens, and using the guide in the table above, draw their reflected/refracted paths. 2. The image is produced at the intersection of the two reflected/refracted rays. Hoo Sze Yen www.physicsrox.com Page 3 of 8 ╞╡§¥ Physics Position of object Between F and the mirror / lens SPM 2015 Chapter 5: Light and Vision Images formed by a Concave Mirror / Convex Lens Ray diagram of concave mirrors Ray diagram of convex lenses Characteristics of image Virtual Upright Magnified At F Virtual Upright Magnified At infinity Real Inverted Magnified Between F and C/ 2F Real Inverted Same size At C / 2F Real Inverted Diminished Greater than C / 2F At infinity Real Inverted Diminished Position of object Anywhere in front of the mirror or lens Images formed by a Convex Mirror / Concave lens Ray diagram of convex mirror Ray diagram of concave lens Characteristics of image Virtual Upright Diminished Hoo Sze Yen www.physicsrox.com Page 4 of 8 Chapter 5: Light and Vision ╞╡§¥ Physics SPM 2015 SUMMARY OF COMPARISON OF IMAGE CHARACTERISTICS Characteristics of concave mirrors are the same as convex lenses: Lens / Mirror 2f Real, Inverted Diminished f Virtual, Upright Magnified Same size Object distance Image characteristics u=∞ Real Inverted Diminished u > 2f Real Inverted Diminished u = 2f Real Inverted Same Size f < u < 2f Real Inverted Magnified u=f Virtual Upright Magnified u<f Virtual Upright Magnified Characteristics of convex mirrors are the same as concave lenses: Virtual, Upright, Diminished Hoo Sze Yen www.physicsrox.com Page 5 of 8 ╞╡§¥ Physics Chapter 5: Light and Vision SPM 2015 5.1.4 Lens Equation Focal length, f Convex lens: positive Concave lens: negative 1 1 1 u v f where u = object distance [cm] v = image distance [cm] f = focal length of lens [cm] Object distance, u Always positive 5.1.5 Lens Power P 1 f where P = lens power [D] f = focal length [m] P OR Image distance, v If positive: real image If negative: virtual image 100 f where P = lens power [D] f = focal length [cm] 5.1.6 Linear Magnification Linear magnification is the ratio of the image size to the object size. m |m| > 1: magnified |m| = 1: same size |m| < 1: diminished hi v ho u where m = linear magnification hi = height of image ho = height of object 5.1.7 If m is negative, take the modulus value Application of Lenses Complex Microscope fo < fe Astronomical Telescope fo > f e Magnification = fo fe Normal setting: Length between lenses = fo + fe Hoo Sze Yen www.physicsrox.com Page 6 of 8 ╞╡§¥ Physics 5.2 Chapter 5: Light and Vision SPM 2015 Refraction and Total Internal Reflection Light refraction is a phenomenon where the direction of light is changed when it crosses the boundary between two materials of different optical densities. It occurs as a result of a change in the speed of light as it passes from one medium to another. When a light ray travels from medium A to When a light ray travels from medium C to medium B which is optically denser than A medium D which is optically denser than C The ray of light will refract towards normal; r < i The ray of light will refract away from normal; r > i When a light ray crosses the boundary between two different mediums at a right angle i = 0°, r = 0° 5.2.1 Snell’s Law Snell’s Law states that the ratio of sin i to sin r is a constant. sin i = constant sin r 5.2.2 Refractive Index The refractive index or index of refraction of a medium is equivalent to the optical density of a medium. Note: A material with greater density may not necessarily have greater optical density. The refractive index / index of refraction of a medium, n can be calculated as: n = sin i sin r speed of light in air, c speed of light in the medium, v actual depth, D = apparent depth, d 1 = sin c = (where c is the critical angle) Hoo Sze Yen www.physicsrox.com Page 7 of 8 ╞╡§¥ Physics Chapter 5: Light and Vision SPM 2015 5.2.3 Total Internal Reflection Critical angle, c is the value of the incident angle when the refracted angle is 90°. • • When i is increased to be greater than c, the light will be complete reflected back into the material. No light will be refracted. This phenomenon is known as total internal reflection. Conditions for total internal reflection: 1. Light must be traveling from an optically denser medium to a less dense medium. 2. The incident angle must be greater than the critical angle. END OF CHAPTER Hoo Sze Yen www.physicsrox.com Page 8 of 8