Physics 106 Lesson #26 Dr. Andrew Tomasch 2405 Randall Lab [email protected] Optics: Optical Instruments.

Physics 106 Lesson #26

Dr. Andrew Tomasch

2405 Randall Lab

[email protected]

Optics:Optical Instruments

Propagation of Light Waves

• Light waves arrive at objects and interact with them in three basic ways. They can:

1. Reflect (bounce off)

2. Refract (go through)

3. Be absorbed (stop)

• Not exclusive, all three may occur

Demonstration

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.

i r

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

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

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

c cn v

v n

INDEX OF REFRACTION

Refraction at Surface of Water

http://www.opticalres.com/gentsupp_f.html

Refraction and the Normal Direction

• Light bends toward the normal when passing from a lower into a higher index of refraction

Air: n = 1.00

Water: n = 1.33

Normal Direction to Air- Water Surface

Light Ray Bends Toward the Normal in Water

Demonstration

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?

1) Beyond where the fish appears

2) In front of where the fish appears

3) Directly where the fish appears

Concept Test #1

Where the fish really is

Where the fish really is

What you see

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.

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

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.

1 1 1

i o f

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

A Double Rainbow…

The Spectrum of a Prism

White light is a combination of all the visible colors

nr< no < ny < ng < nb < ni <nv

Which statement about the relative speed of light traveling in a glass prism is true?

1) Red and violet light travel at the same speed.

2) Violet light travels faster than red light

3) Red light travels faster than violet light.

Concept Test #2

Where the fish really is

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.

nr< no < ny < ng < nb < ni <nv

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”

+ =

Spherical Mirrors• Spherical mirrors are curved mirrors which

are sections of a sphere.• Two types of spherical mirrors:

1) Concave (insideinside surface is reflective)

2) 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!)

Spherical Mirrors

• 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

Concave Convex

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

1 1 1

i o f

Concave Convex

•Light from an object outside the focal point of a converging mirror will be focused to a real image in front of the mirror.

Concave Mirrors: Real Images

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.

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

• 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

The Compound Microscope

1630

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

objective

eyepiece

fM

f

M is the Angular Magnification

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

objective

eyepiece

fM

f

Newtonian Reflecting Telescope

Parabolic Objective Mirror Flat Mirror

Eyepiece

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

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

Other Telescopes

Schmidt-Newton

Newton-Cassegrain