Reflection and Mirrors Flashcards
Law of Reflection
angle of incidence = angle of reflection
Fermat’s Principle
-light travels between two points along the path that requires the least time as compared to other nearby paths
Fermat’s Principle
Reflection
-can be used to derive the law of reflection
angle of incidence = angle of reflection
Total Internal Reflection
-occurs when a wave in a medium with a high refractive index enters a medium with a lower refractive index
-incident angle for which this occurs is the critical angle θc
n1sinθ = n2sin90
Optical Fibres vs. Radio Signals
-a transmission system using light of ~1014Hz can transmit information at a much greater rate than one using radio waves which have frequency ~106Hz
Fermat’s Principle
Refraction
-can be used to derive Snell’s law of refraction
sinθ2 / sinθ1 = n1 / n2
How do we judge an object’s position?
-always have to use more than one ray
Images Formed by Plane Mirrors
- light comes form a point source P and is reflected by the mirror
- to the eye, the light now appears as if it came from an object P’ inside to the mirror
- P’ is the image of object P in the mirror, it is a virtual image
Real Images
- occur where light rays intersect
- can be displayed on a screen
Virtual Images
- occur at an apparent point of origin of light rays
- cannot be displayed on a screen
- an image in a plane mirror is virtual for a real object
Mirrors and Multiple Images
- two mirrors at an angle to each other form multiple images
- rays from an object P are reflected by a plane mirror 1, forming an image P1’
- light from P reflected from mirror 2 creates an image, P2’
- rays reflected form mirrors 1 and 2 form an image P12’’
- P12’’ is an image of P1’ in mirror 2
Spherical Mirrors - Paraxial Rays
- the paraxial rays (rays almost parallel to the principle axis) are focused by a spherical mirror
- non-paraxial rays are not focused by a spherical mirror and instead blur the image, spherical abberation
Concave Mirrors
Principle Axis and Vertex
Principle Axis - straight line through the centre of the curve of the mirror
Vertex - the middle of the mirror surface
Concave Mirrors
Centre and Radius of Curvature
Centre of Curvature - centre of the sphere that the curved surface of the mirror forms
Radius of Curvature - the radius of the sphere that the curved surface of the mirror forms
Seeing Real and Virtual Images
- if an image is real it will show up on a screen placed there because light from the object is really concentrated there
- the eye sees both real and virtual images as if they are objects
Concave Mirror
Image of an Extended Object
- object points upwards from the principle axis
- consider two light rays form the object
i) a ray from the top of the object through the centre of curvature, it is incident normal to the mirror so is reflected back on itself
ii) a ray drawn from the top of the object that strikes the mirror at the vertex, it is incident at an angle θ above the principle axis so is reflected at an angle θ below the principle axis - the image is at the point where these two lines intersect
Concave Mirror
Lateral Magnification
m = h’ / h = -s’ / s
h = height of the object
h’ = height of the image (negative as below the principle axis
s = distance of the object from the vertex along the principle axis
s’ distance of the image from the vertex
The Mirror Equation
1/s’ + 1/s = 2/r = 1/f
r = the distance between the centre of curvature and the vertex, a property of the mirror s' = distance of the image from the vertex s = distance of the object from the vertex f = focal length
-if an image is a long way from the mirror, s»r, then rays from the object become parallel
Focal Point and Focal Length
- parallel rays are brought to a focus halfway between the mirror and the centre of curvature at the focal point, F
- the distance of F from the mirror is the focal length given by, f =r/2
Ray Diagrams for Concave Mirrors
- an image is found using principle rays
1) Parallel Ray - parallel to the axis, reflected through the focal point
2) Focal Ray - ray through the focal point, then reflected parallel to the axis
3) Radial Ray - through the centre of curvature and reflected back on itself - the point where these three rays cross is the location of the image
Concave Mirror
Virtual Image
-occurs when s
Convex Mirror
-parallel rays directed towards the convex surface, on reflection they appear to be spreading out from the focal point behind the mirror
Convex Mirror
Ray Diagram
- the centre of curvature is behind the mirror, so the distance between the centre of curvature and the vertex is negative
- the focal point, F, is also behind the mirror so the focal length f is also negative
s
positive or negative
positive s = object in front of mirror, real
negative s = object behind mirror, virtual
s’
positive and negative
positive s’ = image in front of mirror, real
negative s’ = image behind the mirror, virtual
f, r
positive and negative
f, r positive = C & F in front of the mirror, concave
f, r negative = C & F behind the mirror, convex
m
positive and negative
positive m = upright
negative m = inverted
