1. Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu
Physics 106 Lesson #26
Optics:
Optical Instruments
Dr. Andrew Tomasch
2405 Randall Lab

2. Propagation of Light Waves
Light waves arrive at objects and interact with them in three basic ways. They can:
Reflect (bounce off)
Refract (go through)
Be absorbed (stop)
Not exclusive, all three may occur
Demonstration

3. The Law of Reflection
The incident ray, reflected ray and the normal to the surface are all in the same plane.
The angle of incidence equals the angle of reflection.

4. Plane Mirrors
A ray of light from the top of the chess piece reflects from the mirror
To the eye, the ray seems to come from behind the mirror
Because none of the rays actually emanate from the image, it is called a virtual image

5. Refraction
As light passes from one medium to another it changes direction at the interface between the two media
This change of direction is known as refraction

6. The Index of Refraction
Light travels through materials at a speed less than its speed in a vacuum
Indices of Refraction
Vacuum
1 (exactly)
Air
1.0003
Water
1.333
Ice
1.309
Glass
1.523
Diamond
2.419
INDEX OF REFRACTION

7. Refraction at Surface of Water

8. Refraction and the Normal Direction
Light bends toward the normal when passing from a lower into a higher index of refraction
Normal Direction to Air- Water Surface
Air: n = 1.00
Light Ray Bends Toward the Normal in Water
Water: n = 1.33
Demonstration

9. Concept Test #1
While boating on the Amazon, you decide to go spear fishing. You look into the water and see where a fish appears to be. Where should you aim your spear?
Beyond where the fish appears
In front of where the fish appears
Directly where the fish appears
What you see
Where the fish really is
Where the fish really is

10. A Thin Converging Lens Produces a Real, Inverted Image for Objects Outside the Focal Length
A Thin Converging Lens Has a Positive Focal Length-a Real Image can be Produced on the Side Opposite the Object.

11. A Thin Converging Lens Produces a Virtual, Upright Image for Objects Inside the Focal Length

12. The Thin Lens Equation
Relates the Image Distance (i), the Object Distance (o) and the Focal Length (f)
Works for both Converging and Diverging lenses provided the focal length for a Diverging lens is defined to be negative.

13. Dispersion
The index of refraction for a given material will vary with the wavelength of the light passing through it
This means that different colors of light will be refracted through different angles when passing through the same medium.
This is called dispersion and can be demonstrated with a prism or by observing a rainbow

14. A Double Rainbow…

15. The Spectrum of a Prism
White light is a combination of all the visible colors
nr< no < ny < ng < nb < ni <nv

16. Concept Test #2 n=c/vglass so the larger the refractive index,
Which statement about the relative speed of light traveling in a glass prism is true?
Red and violet light travel at the same speed.
Violet light travels faster than red light
Red light travels faster than violet light.
n=c/vglass so the larger the refractive index,
the slower the speed. Red light has a lower
refractive index, so it travels faster than violet light.
Where the fish really is
nr< no < ny < ng < nb < ni <nv

17. + = Chromatic Aberration
The dispersion of light as it passes through a refracting lens causes the different colors of light to have different focal lengths - red focuses long and violet focuses short
This undesirable effect causes color “halos” around the images and is called “chromatic aberration” (“color error”)
Coating the lens with thin films of different refractive indices can partially correct for this - “color- corrected coated optics” + =

18. Spherical Mirrors
Spherical mirrors are curved mirrors which are sections of a sphere.
Two types of spherical mirrors:
Concave (inside surface is reflective)
Convex (outside surface is reflective)
Ray tracing shows that the focal length of a spherical mirror is one half the radius of the sphere: f = R/2 (simple!)

19. Spherical Mirrors Concave Convex
Parallel light rays striking a spherical mirror converge upon or diverge from a focal point
Concave: real focus, light converges
Convex: virtual focus, light diverges

20. The Thin Lens Equation Works for Spherical Mirrors
Concave (converging) mirrors have a positive focal length and can produce real images
Convex (diverging) mirrors have a negative focal length and cannot produce real images
Concave
Convex

21. Concave Mirrors: Real Images
Light from an object outside the focal point of a converging mirror will be focused to a real image in front of the mirror.

22. Concave Mirrors: Virtual Images
When an object is located inside the focal point of a concave mirror, an enlarged, upright, and virtual image is produced which appears to be behind the mirror.

23. Instruments: Multiple Lenses and Mirrors
Strategy: Form a real first image with one lens or mirror and then hold a magnifier up to the real image to produce a final magnified virtual image

24. The Compound Microscope
A small object is placed just outside of a short focal length (high diopter power) objective lens and the resulting real first image is viewed with a second short focal length eyepiece lens
1630

25. The Refracting Telescope
A first real image of a distant object is formed by a long focal length (low diopter power) objective lens. The first real image is then viewed with a second short focal length (high diopter power) eyepiece lens
M is the Angular Magnification

26. The Newtonian Reflecting Telescope
A first real image of a very distant (“at infinity”) object is formed by a long focal length (low diopter power) objective mirror. The first real image is then viewed with a second short focal length (high diopter power) eyepiece lens
The first real image is brought to the side by means of a small flat mirror so that the eyepiece and observer can be out of the way of the incoming light
Newtonian Reflecting Telescope
Parabolic Objective Mirror
Flat Mirror
Eyepiece

27. Spherical Aberration
Lenses and mirrors with spherical surfaces are easy to make and understand, but they do not actually focus all incoming rays to a single point. This effect is called spherical aberration and is responsible for the “fish eye” distortion seen through a clear marble.
Newton understood this effect and therefore based his reflecting telescope on an objective mirror with a parabolic shape, which has a perfect single point focus
Parabolic mirrors are optically perfect, introducing neither spherical nor chromatic aberration, but they are very difficult and expensive to make
Another approach is to “correct the vision” of a spherical mirror—The Schmidt Camera

28. The Schmidt Camera
Schmidt was a 19th Century optician who ground spectacles by day and astronomical telescopes by night
His “corrector plate” eliminates spherical aberration and is too not difficult to make

29. Other Telescopes
Schmidt-Newton
Newton-Cassegrain