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╞╡§¥ Physics
Chapter 5: Light and Vision
SPM 2013
CHAPTER 5: LIGHT AND VISION 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: Image is exactly the same size as the object Same 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 Image appears upside down compared to object Inverted Real images are images you can capture on a screen. Real Type Virtual
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 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
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SPM 2013
Chapter 5: Light and Vision
5.1.3 Curved Mirrors vs Lenses Concave mirror
Also known as Focal lengths
Convex mirror
Converging mirrors
Diverging mirror
Positive E.g. f = +20cm.
Negative E.g. f = -20cm.
Convex lens
Also known Converging lens as Focal Positive lengths E.g. f = +20cm.
Concave lens
Diverging lens Negative E.g. f = -20cm.
For both concave and convex mirrors, the focal length is half the radius; i.e. CF = FP.
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SPM 2013
Chapter 5: Light and Vision
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
A ray through C is reflected back along its own path
Convex mirror
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
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
A ray through C travels straight along its own path
Concave lens
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.
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Position of object Between F and the mirror / lens
SPM 2013
Chapter 5: Light and Vision
Images formed by a Concave Mirror / Convex Lens Ray diagram of concave Ray diagram of convex mirrors 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 Ray diagram of concave mirror lens
Characteristics of image Virtual Upright Diminished
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Chapter 5: Light and Vision
SPM 2013
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
Characteristics of convex mirrors are the same as concave lenses: Virtual, Upright, Diminished
u = object distance [cm] v = image distance [cm] f = focal length of lens [cm]
Object distance, u Always positive Image distance, v If positive: real image If negative: virtual image
5.1.5 Lens Power
P where
1 f
P = lens power [D] f = focal length [m]
P OR where
100 f
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. h v m i ho u where
m = linear magnification hi = height of image ho = height of object
5.1.7
Application of Lenses
m > 1: magnified m = 1: same size m < 1: diminished
Complex Microscope fo < fe
Astronomical Telescope fo > f e Magnification =
fo fe
Normal setting: Length between lenses = fo + fe
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5.2
SPM 2013
Chapter 5: Light and Vision
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 When a light ray travels from medium C to medium B which is optically denser to medium D which is optically denser than A than C
The ray of light will refract towards The ray of light will refract away from normal; r < i 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
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Chapter 5: Light and Vision
SPM 2013
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:
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
n =
(where c is the critical angle)
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
