1. Notation for Mirrors and Lenses
The object distance is the distance from the object to the mirror or lens
Denoted by p
The image distance is the distance from the image to the mirror or lens
Denoted by q
The lateral magnification of the mirror or lens is the ratio of the image height to the object height
Denoted by M

2. Images
Images are always located by extending diverging rays back to a point at which they intersect
Images are located either at a point from which the rays of light actually diverge or at a point from which they appear to diverge

3. Types of Images
A real image is formed when light rays pass through and diverge from the image point
Real images can be displayed on screens
A virtual image is formed when light rays do not pass through the image point but only appear to diverge from that point
Virtual images cannot be displayed on screens

4. Images Formed by Flat Mirrors
Simplest possible mirror
Light rays leave the source and are reflected from the mirror
Point I is called the image of the object at point O
The image is virtual

5. Images Formed by Flat Mirrors
One ray starts at point P, travels to Q and reflects back on itself
Another ray follows the path PR and reflects according to the law of reflection
The triangles PQR and P’QR are congruent

6. Lateral Magnification
Lateral magnification, M, is defined as
This is the general magnification for any type of mirror
It is also valid for images formed by lenses
Magnification does not always mean bigger, the size can either increase or decrease
M less than 1 -> image size decreased
M greater than 1 -> image size increased

7. Reversals in a Flat Mirror
A flat mirror produces an image that has an apparent left-right reversal
For example, if you raise your right hand the image you see raises its left hand

8. Spherical Mirrors
A spherical mirror has the shape of a section of a sphere
The mirror focuses incoming parallel rays to a point
A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve
A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve

9. Convex vs Concave

10. Spherical aberation
No clear focusing of the incident rays

11. Spherical mirrors R

12. Spherical Mirrors d S C P F

13. Ray Tracing Parallel ray hit the mirror and heads to the focus
Ray through focus hits the mirror and comes off parallel
Ray through center of curvature returns to center of curvature

14. Ray Tracing F C
Parallel ray hits the mirror and reflects as if it started at the focus
Ray heading to the focus hits the mirror and comes off parallel
Ray heading to the center of curvature returns along the same path

15. Magnification
Gain is a better
description since M
might be < 1
Or:

16. Sign Conventions

17. Example: Find the imageC F
f = 20 cm
p = 32 cm
h = 5 cm

18. Images Formed by Refraction

19. Sign Conventions for Refracting Surfaces

20. Flat Refracting Surfaces
If a refracting surface is flat, then R is infinite
Then q = -(n2 / n1)p
The image formed by a flat refracting surface is on the same side of the surface as the object
A virtual image is formed

21. Locating the Image Formed by a Lens
The lens has an index of refraction n and two spherical surfaces with radii of R1 and R2
R1 is the radius of curvature of the lens surface that the light of the object reaches first
R2 is the radius of curvature of the other surface
The object is placed at point O at a distance of p1 in front of the first surface
Small!!

22. Lens Makers’ Equation
The focal length of a thin lens is the image distance that corresponds to an infinite object distance
This is the same as for a mirror
The lens makers’ equation is

23. Thin lenses - converging

24. Thin lenses - diverging

25. Ray Tracing Rules
A ray parallel to the axis exits through the focal point
A ray through the focal point leaves parallel to the axis
A ray through the center is undeviated

26. Ray Diagram for Converging Lens, p < f
The image is virtual
The image is upright
The image is larger than the object
The image is on the front side of the lens

27. Ray tracing for a diverging lens

28. Sign Conventions

29. Example
A 2 cm tall object is placed 30 cm in front of a diverging lens with a focal length of –20 cm. Find the location of the image, its classification, the size of the image, and the magnification. Construct a ray diagram.

30. Lateral (Transverse) magnificationh h’
But:
Or:

31. Multiple Thin Lenses Find the image distance of the first lens.
Use the image of the first lens as the object of the second lens.
Find the new object distance by correcting with the separation of the lenses.
Find the image of the second lens.
Transverse Magnification is the product of the magnifications of the individual lenses

32. Example
Find the location and magnification of the final image formed

33. 9. A spherical convex mirror has a radius of curvature with a magnitude of 40.0 cm. Determine the position of the virtual image and the magnification for object distances of (a) 30.0 cm and (b) 60.0 cm. (c) Are the images upright or inverted?
11. A concave mirror has a radius of curvature of 60.0 cm. Calculate the image position and magnification of an object placed in front of the mirror at distances of (a) 90.0 cm and (b) 20.0 cm. (c) Draw ray diagrams to obtain the image characteristics in each case.
12. A concave mirror has a focal length of 40.0 cm. Determine the object position for which the resulting image is upright and four times the size of the object.

34. 29. The left face of a biconvex lens has a radius of curvature of magnitude 12.0 cm, and the right face has a radius of curvature of magnitude 18.0 cm. The index of refraction of the glass is (a) Calculate the focal length of the lens. (b) What If? Calculate the focal length the lens has after is turned around to interchange the radii of curvature of the two faces.
31. A thin lens has a focal length of 25.0 cm. Locate and describe the image when the object is placed (a) 26.0 cm and (b) 24.0 cm in front of the lens.
34. A person looks at a gem with a jeweler’s loupe—a converging lens that has a focal length of 12.5 cm. The loupe forms a virtual image 30.0 cm from the lens. (a) Determine the magnification. Is the image upright or inverted? (b) Construct a ray diagram for this arrangement.