Introduction to Mirrors SPH3UW: OPTICS I Introduction to Mirrors 1

Light incident on an object Absorption Reflection (bounces)** See it Mirrors Refraction (bends) Lenses Often some of each Everything true for wavelengths << object size

qi = qr Reflection Angle of incidence = Angle of reflection (Angles between light beam and normal) qi qr Before this slide, bounce pass basket ball

We know object’s location by the direction the light rays come from. Object Location Light rays from sun bounce off object and go in all directions Some of the rays hit your eyes We know object’s location by the direction the light rays come from. Color: some light is absorbed by object before bouncing off.

Reflection from a Plane Mirror The angle of incidence equals the angle of reflection. This assumes the surface is perfectly smooth.

Diffuse Reflection When the surface is rough, the surface at any point makes some angle with respect to the horizontal. The angle of incidence still equals the angle of reflection.

Plane Mirrors In the left hand picture with a rough surface, you can place your eye anywhere and you will see some reflected rays. On the right hand side, you eye has to be in the correct position to see the reflected light. This is called specular reflection.

Plane Mirrors A plane mirror provides the opportunity to fool you by making your eye and brain perceive an image.

Plane Mirrors The image appears to be the same distance behind the mirror as the object is in front of the mirror.

Plane Mirrors The image is called a virtual image because if you placed a piece of paper at the image location, you wouldn’t see any light.

Plane Mirror All you see is what reaches your eyes Image Object You think object’s location is where rays appears to come from. qr qi All rays originating from peak will appear to come from same point behind mirror! Image Object

How to Draw the Image in a Plane Mirror (1) Draw first ray perpendicular to mirror qi =00= qr (2) Draw second or third ray at angle. qi = qr (3) Where the extended lines appear to intersect (a distance d behind mirror) is the image location. Light rays don’t really converge there, so it’s a “Virtual Image” Virtual: No light actually gets here. Here can do cool light with ½ silvered mirror demo. qr qi qr d qi

How Big a Mirror? 0.80 m

Question Why do ambulances have “AMBULANCE” written backwards?

So you can read it in your rear-view mirror! Solution Might change Virtual Image definition “Light rays don’t actually intersect at image location.” So you can read it in your rear-view mirror!

Question Can you see Fido’s tail in mirror? mirror (You) (Fido)

No! Solution Can you see Fido’s tail in mirror? (You) (Fido) mirror You need light rays from the tail to bounce off mirror and reach your eye! (You) (Fido)

ACT: Plane Mirrors You are standing in front of a short flat mirror which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move: (1) closer to the mirror. (2) further from the mirror. (3) to another mirror.

ACT: Plane Mirrors You are standing in front of a short flat mirror which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move: (1) closer to the mirror. (2) further from the mirror. (3) to another mirror. Changing distance doesn’t change what you see of yourself

Two Mirrors How many images of money will you see (not including the actual money)?

Two Mirrors How many images of money will you see (not including the actual money)? 2 1 3

Curved mirrors • • A Spherical Mirror: section of a sphere. principal axis light ray • Concave mirror R C R Convex mirror principal axis light ray R C • C = Center of Curvature In front of concave mirror Behind convex mirror.

Understanding An organic chemistry student accidentally drops a glass marble into a silver nitrate mirroring solution, making the outside of the marble reflective. What kind of mirror is this? (1) concave (2) convex (3) flat

Concave Mirror Focus Principal Axis f=R/2 Rays are bent towards the principal axis. Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they pass through the “Focus” (F). The distance from F to the center of the mirror is called the “Focal Length” (f).

Understanding What kind of spherical mirror can be used to start a fire? concave convex How far from the paper to be ignited should the mirror be held? farther than the focal length closer than the focal length at the focal length

Concave Mirror F F Principal Axis Rays traveling through focus before hitting mirror are reflected parallel to Principal Axis. Rays traveling parallel to Principal Axis before hitting mirror are reflected through focus

Convex Mirror Principal Axis Focus f=-R/2 Rays are bent away from the principal axis. Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they appear to originate from the “Focus” (F). The distance from F to the center of the mirror is called the “Focal Length” (f).

Concave Mirror –Drawing image When object is on the outside of the centre of curvature Technique 1) Parallel to principal axis reflects through f. #3 2) Through f, reflects parallel to principal axis. #2 #1 3) Through center. 4) At the vertex f V c Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged Comment that this is “weird” to have a real image. #4 **Every other ray from object tip which hits mirror will reflect through image tip. You need at least two of the above techniques to draw image

Concave Mirror –Drawing image When object is on the outside of the centre of curvature The image is real The image is inverted The image is smaller than the object

Concave Mirror-Drawing images When object is at the centre of curvature Technique 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. #1 #2 3) At the vertex f c V Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged or Same Size #3 **Every other ray from object tip which hits mirror will reflect through image tip

Concave Mirror-Drawing images When object is between the centre of curvature and the focus Technique 1) Parallel to principal axis reflects through f. #2 2) Through f, reflects parallel to principal axis. #1 3) At the vertex f V c Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged #3 **Every other ray from object tip which hits mirror will reflect through image tip

Concave Mirror Principal Rays When object is between the focus and the Vertex Technique 1) Parallel to principal axis reflects through f. 2) Through f, reflects parallel to principal axis. #1 3) At the vertex f V c Image is (in this case): Real or Imaginary Inverted or Upright Reduced or Enlarged #2 #3 **Every other ray from object tip which hits mirror will reflect through image tip

Concave Mirror Principal Rays When object is between the focus and the Vertex The image is virtual The image is upright The image is larger than the object

Which ray is NOT correct? Understanding Which ray is NOT correct? p.a. 1) R f 2) 3) Ray through centre should reflect back on self.

Mirror Focal Lengths A concave mirror has a positive focal length f > 0 A convex mirror has a negative focal length f < 0 What is the focal length of a flat mirror? (1) f =0 (2) f = ∞ The flatter the mirror, the larger the radius of curvature, (e.g. the earth is round, but looks flat)

Concave Mirror Image Location Yep, no image

Mirror Equation do O f c I do = distance object is from mirror: Positive: object is _______ of mirror Negative: object is _______ mirror In front behind di di = distance image is from mirror: Positive: _______ image is __________ of mirror Negative: _______ image is__________ mirror inverted In front Inverted upright upright behind f = focal length mirror: Positive: _________ mirror Negative: _________ mirror Concave Convex In Front Behind concave convex

Understanding The image produced by a concave mirror of a real object is: Always Real Always Virtual Sometimes Real, Sometimes Virtual Mirror Equation In a concave mirror the focal length, f, is >0 Real Object means in front of mirror: do > 0 Therefore di can be positive or negative

Practice: Concave Mirror Where in front of a concave mirror should you place an object so that the image is virtual? Mirror Equation: Close to mirror Far from mirror Either close or far Not Possible In a concave mirror the focal length, f, is > 0 Object in front of mirror: do > 0 Virtual image means behind mirror: di < 0 When do < f then di <0 : virtual image.

Magnification Equation do O do ho Angle of incidence ho = height of object: Positive:_______________ q Always di hi Angle of reflection I q hi = height of image: Positive: ______________ Negative: _____________ upright inverted m = magnification: Positive / Negative: same as for hi < 1: image is _______________ > 1: image is ________________ di reduced q enlarged q

Practice Solving Equations A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location. Real Image! (in front of mirror) Compared to the candle, the image will be: Larger Smaller Same Size p.a. C f Note: image is 3 cm in front of mirror, therefore 1 cm to the left of the focus

Practice: Magnification A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2. What is the size of the image? 2 inches 4 inches 8 inches 4 inches Magnitude gives us size. What direction will the image arrow point? Up 2) Down (-) sign tells us it’s inverted from object

Convex Mirror Rays Technique 1) Parallel to principal axis reflects through f. 2) Through center. #1 3) Through f, reflects parallel to principal axis. O #2 I #3 f c Make this mirror almost flat so that it is like your rearview mirror Image is: Virtual (light rays don’t really cross) Upright (same direction as object) Reduced (smaller than object) (always true for convex mirrors!):

Convex Mirror Rays The image is virtual The image is upright The image is smaller than the object

Convex Mirror Images Unlike Concave Mirrors, convex mirrors always produce images which share these characteristics. The location of the object does not affect the characteristics of the image. As such, the characteristics of the images formed by convex mirrors are easily predictable The diagrams below shows that in each case: the image is located behind the convex mirror a virtual image an upright image reduced in size (i.e., smaller than the object)

Overview Reflection: qi = qr Refraction: n1 sin(q1)= n2 sin(q2) Last Time qi qr qi = qr Flat Mirror: image equidistant behind Spherical Mirrors: Concave or Convex Today q1 q2 n2 n1 Next time Refraction: n1 sin(q1)= n2 sin(q2) Flat Lens: Window Spherical Lenses: Concave or Convex Absorption

Solving Problems Virtual Image! Image is Upright! A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location. Determine the magnification of the candle. If the candle is 9 cm tall, how tall does the image candle appear to be? di = - 2 cm (behind mirror) Virtual Image! Image is Upright!

Problem Where should you place an object in front of a convex mirror to produce a real image? Mirror Equation: Object close to mirror Object far from mirror Either close or far You can’t di is negative! f is negative do is positive Convex mirror: f < 0 Object in front of mirror: do > 0 Real image means di > 0

Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f

Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f The image is 17 cm in front of the mirror

Problem A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f The height of the inverted image is 1.1 cm

Problem A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f

Problem A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f Therefore the image is 0.37 m behind the mirror

Problem A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror. At What distance from the mirror will the image be formed? What is the height of the image? C f

Mirror Summary Angle of incidence = Angle of Reflection Principal Rays Parallel to P.A.: Reflects through focus Through focus: Reflects parallel to P.A. Through center: Reflects back on self |f| = R/2