Chapter 36 Mirrors and Image Formation

1. Chapter 36 Mirrors and Image Formation PHYS 2326-31

2. Concepts to Know • Mirrors • Plane, Concave, Convex • Sign Conventions • Object Distance • Image Distance • Focal Length • Magnification

3. Concepts to Know • Enlarged, Reduced • Erect, Inverted • Real, Virtual • Reversed (Perverted) • Converging, Diverging • Aberration • Principle Rays

4. Definitions • Plane surface = one that is flat • Concave surface, one that is curved inward at the center • Convex surface, one that is curved outward Eye Plane Concave Convex

5. Eye Objects & Images p q • Image from a Plane Mirror • p object to surface, q surface to image • h object height, h’ image height • Magnification M = 1 for flat mirror h h’ θ Object θ Image

6. Images • Virtual Image - no light reaches image • Real Image - light rays reach image • Erect or Upright Image – directions unchanged (object up is same direction as image up) • Inverted Image – directions opposite (object up is image down) • Reversed Image – left seems right

7. Spherical Mirrors • Parameters of a spherical mirror • Principal axis – line through C and V where V is the center of the mirror • C – Center of Curvature – center of sphere or circle (2 dimensions) • R – Radius of Curvature • F – Focal point • Radius lines are always normal to surface of circles and spheres V R C principal axis F Concave

8. Given an object to the left of C, by the law of reflection, θ= θ’, light rays will converge at a point between V and C for rays with small angles to the principal axis • For larger angles the rays will intersect at different points creating spherical aberration – See Fig. 36.8 V C principal axis O I Concave

9. Image Concave Mirror • Rays through C are normal to surface θ=0 • Draw rays to V (intersection of surface and principal axis) θ= θ’ and through C, θ=0 • Tan θ = h/p = -h’/q, since M = h’/h, = -q/p • Note -h’ = inverted • Image is • smaller • inverted • real • outside point F Concave p R h V θ α α h’ θ C F q

10. since tan α = -h’/(R-q) = h/(p-R) h’/h = -(R-q)/(p-R) eqn 36.3 1/p + 1/q = 2/R eqn 36.4 MIRROR EQN For a very distant object where p-> infinity, 1/p ~ 0 so 1/q = 2/R This case it is called the focal point F, where F = 2/R eqn 36.5 hence 1/p + 1/q = 1/f, eqn 36.6, the mirror equation The focal point is where rays parallel to the axis pass through

11. Spherical Convex Mirror • Often called a diverging mirror • Concepts presented are valid for this type of mirror as well if adhere to the following procedure • R, F & q negative • p, h & h’ positive R V C principal axis F p q

12. Procedure • Front side of mirror = where light waves originate and move towards the mirror • Back side is the other side

13. Mirror Sign ConventionsTable 36.1

14. Ray Trace Example 1 • Object outside focal point • Image inverted and smaller • Rays drawn through C, and parallel to principal axis and through F V C F

15. Ray Trace Example 2 • Object is inside the focal point F • Image is virtual, upright and magnified V C F

16. Ray Trace Example 3 • Convex mirror • Image is virtual, reduced and upright R C V F p q

17. Ray Tracing • Principal axis goes through C, center of curvature so is perpendicular to the surface at V. Bottom of object. • Ray 1 top of object parallel to principal axis goes through Focal point or reflects away from focal point for convex mirror • Ray 2 top of object through focal point – reflects parallel to axis where it intersects mirror • Ray 3 top of object through Center of curvature, reflects back on self

18. Example Problem 1 Given object of height 1 cm located 30cm in front of a concave mirror of focal length 10 cm, what is a) radius of curvature? b) Location of image? c) Real/virtual image? d) Magnification? e) Enlarged? f) Image height? g) upright/inverted?

19. V C F h = 1cm, p = 30cm, f=10cm f= R/2, 1/p + 1/q = 1/f M = -h’/h, M= -q/p • R = 2f = 20cm • q = 1/(1/f – 1/p) = 15cm • Real • M = -q/p = -15/30 = -0.5 • Reduced • M=-h’/h , -0.5 = -0.5cm/1cm • Inverted