Reflection and Mirrors

Question 1

Law of Reflection

Answer 1

angle of incidence = angle of reflection

Question 2

Fermat’s Principle

Answer 2

-light travels between two points along the path that requires the least time as compared to other nearby paths

Question 3

Fermat’s Principle

Reflection

Answer 3

-can be used to derive the law of reflection

angle of incidence = angle of reflection

Question 4

Total Internal Reflection

Answer 4

-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

Question 5

Optical Fibres vs. Radio Signals

Answer 5

-a transmission system using light of ~1014Hz can transmit information at a much greater rate than one using radio waves which have frequency ~106Hz

Question 6

Fermat’s Principle

Refraction

Answer 6

-can be used to derive Snell’s law of refraction

sinθ2 / sinθ1 = n1 / n2

Question 7

How do we judge an object’s position?

Answer 7

-always have to use more than one ray

Question 8

Images Formed by Plane Mirrors

Answer 8

• 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

Question 9

Real Images

Answer 9

• occur where light rays intersect

- can be displayed on a screen

Question 10

Virtual Images

Answer 10

• 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

Question 11

Mirrors and Multiple Images

Answer 11

• 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

Question 12

Spherical Mirrors - Paraxial Rays

Answer 12

• 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

Question 13

Concave Mirrors

Principle Axis and Vertex

Answer 13

Principle Axis - straight line through the centre of the curve of the mirror
Vertex - the middle of the mirror surface

Question 14

Concave Mirrors

Centre and Radius of Curvature

Answer 14

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

Question 15

Seeing Real and Virtual Images

Answer 15

• 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

Question 16

Concave Mirror

Image of an Extended Object

Answer 16

• 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

Question 17

Concave Mirror

Lateral Magnification

Answer 17

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

Question 18

The Mirror Equation

Answer 18

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

Question 19

Focal Point and Focal Length

Answer 19

• 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

Question 20

Ray Diagrams for Concave Mirrors

Answer 20

• 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

Question 21

Concave Mirror

Virtual Image

Answer 21

-occurs when s

Question 22

Convex Mirror

Answer 22

-parallel rays directed towards the convex surface, on reflection they appear to be spreading out from the focal point behind the mirror

Question 23

Convex Mirror

Ray Diagram

Answer 23

• 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

Question 24

s

positive or negative

Answer 24

positive s = object in front of mirror, real

negative s = object behind mirror, virtual

Question 25

s’

positive and negative

Answer 25

positive s’ = image in front of mirror, real

negative s’ = image behind the mirror, virtual

Question 26

f, r

positive and negative

Answer 26

f, r positive = C & F in front of the mirror, concave

f, r negative = C & F behind the mirror, convex

Question 27

m

positive and negative

Answer 27

positive m = upright

negative m = inverted