Introduction to Optics Lecture 11

(See Giancoli Chapter 23)

Silas Laycock, UML, General Physics II. Spring 2014. Lecture slides not to be disseminated on the internet or shared

beyond this class

Ray Optics

Reflections and Mirrors

Phenomena involving reflection

Primary colors

•  The primary colors are Red, blue and

yellow •  Green light+ Red light = Yellow light •  Blue light + yellow light = green light

Optics: Summary •  The Ray Model of Light

•  Image formed by a pinhole

•  Reflection; Image Formed by a Plane Mirror

•  Formation of Images by Spherical Mirrors

•  Index of Refraction

•  Refraction: Snell’s Law

•  Total Internal Reflection; Fiber Optics

•  Thin Lenses; Ray Tracing

•  The Thin Lens Equation; Magnification

•  Lens power and diopter

•  Combinations of Lenses (extra)

There are 3 basic ways to gather light and focus it to make an image.

Pinhole - Simple geometry

Mirror - Reflection

Lens - Refraction

Pinhole Camera Image Formation (the pinhole camera is the “perfect” optical system)

•  Pinhole images can form whenever light passes though a small hole.

•  Sunlight falling between the leaves of trees often causes a dappled appearance on the ground. Each of the small round dapples (patches of light) is a perfect focused image of the Sun!

•  In this picture a solar eclipse was in progress so the patches are all crescent shaped.

This pinhole image of a living human (!) was made using gamma rays

The Law of Reflection

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence.

23.2 Reflection; Image Formation by a Plane Mirror

When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection.

The size of this sun patch depends on the roughness of the sea surface

ConcepTest 23.1 Reflection When watching the Moon over

the ocean, you often see a long streak of light on the surface of the water. This occurs because:

1) the Moon is very large 2) atmospheric conditions are

just right

3) the ocean is calm 4) the ocean is wavy 5) motion of the Moon

When the water surface changes, the angle of incidence also changes. Thus, different spots on the water can reflect the Moon into your eyes at different times.

ConcepTest 23.1 Reflection When watching the Moon over

the ocean, you often see a long streak of light on the surface of the water. This occurs because:

1) the Moon is very large 2) atmospheric conditions are

just right

3) the ocean is calm 4) the ocean is wavy 5) motion of the Moon

Follow-up: Where else does this occur?

Reflection; Image Formation by a Plane Mirror

With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position.

Munch’s “Girls on the Pier” Painting

Reflection; Virtual Images

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror.

Notice how many ways mirror images differ from a direct view of the scene

ConcepTest 23.2b Mirror II You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely?

1) same as your height

2) less than your full height but more than half your height

3) half your height

4) less than half your height

5) any size will do

ConcepTest 23.2b Mirror II

Trace the light rays from the image’s foot to the mirror and then to the eye. Since we know that θi = θr , you need a mirror only half your size.

You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely?

1) same as your height

2) less than your full height but more than half your height

3) half your height

4) less than half your height

5) any size will do

ConcepTest 23.2c Mirror III

Does this depend on your distance from the mirror?

1) No.

2) Yes.

3) Depends on the mirror.

4) Depends on the person.

ConcepTest 23.2c Mirror III

Does this depend on your distance from the mirror?

1) No.

2) Yes.

3) Depends on the mirror.

4) Depends on the person.

The further you step back, the smaller the incident and reflected angles will be. But the rays will still be reflected at the same points, so the ray from the foot will still be reflected at mid-height.

Formation of Images by Spherical Mirrors

Spherical mirrors are shaped like sections of a sphere, and may be reflective on either the inside (concave) or outside (convex).

Try this yourself, next time you have a spoon in your hand.

Compare to what you see in a shaving/makeup mirror.

Is the Convex image ALWAYS erect, and the Concave ALWAYS inverted?

______ Mirrors always produce an erect image, ______ mirrors can produce an inverted image or an erect image depending on the viewing distance.

A.  Convex, Concave

B.  Flat, Convex

C.  Concave, Convex

23.3 Formation of Images by Spherical Mirrors

Rays coming from a faraway object are effectively parallel.

23.3 Formation of Images by Spherical Mirrors

Parallel rays striking a spherical mirror converge at a point, called the Focus, or focal point.

The law of reflection does not depend on the wavelength of light, so mirrors produce perfect color images (no chromatic aberration)

If the curvature of the mirror is large, the point becomes spread out. This is called spherical aberration.

Radius of Curvature and Focal Length

Focal Length of a Spherical Mirror

•  A deeper curve gives a shorter focal length

•  Using geometry, we find that the focal length is half the radius of curvature:

•  Spherical aberration can be avoided by using a parabolic reflector; which are only a little more difficult/expensive to make.

•  Typically used in Telescopes, Camera lenses Lab equipment, shaving/make-up Mirrors, and this solar fire-lighter for campers!

•  Mirrors are preferred to lenses in many applications because of their perfect color rendition, greater maximum size, and substantially lower cost.

23.3 Formation of Images by Spherical Mirrors

We use ray diagrams to determine where an image will be. For mirrors, we use three key rays, all of which begin on the object:

1.  A ray parallel to the axis; after reflection it passes through the focal point

2.  A ray through the focal point; after reflection it is parallel to the axis

3.  A ray perpendicular to the mirror; it reflects back on itself

The Mirror Equation

Geometrically, one can derive an equation that relates the object distance, image distance, and focal length of the mirror:

(23-2)

Focal Length is the most important characteristic of an any optical element. It is the distance from the mirror (or lens) surface at which a distant object is brought to focus.

The More strongly curved the surface, the more it bends the light rays.

Steep curve = short focal length

Magnification by Mirrors and simple lenses

Magnification is the ratio of image height to object height. (this is an “obvious” definition)

Less obvious but more useful: This ratio is the same as the ratio of Image distance to Object distance!

(23-3)

A negative sign indicates that the image is inverted.

-1 < m < 1 means the image is smaller than the object.

Magnification = -0.5 means what?

A.  Image is twice the height of the object, and upside down.

B.  Image is half the height of the object.

C.  Image is half the height of the object, and upside down.

D.  Image is half the area of the object.

23.3 Formation of Images by Spherical Mirrors

If an object is outside the center of curvature of a concave mirror, its image will be inverted, smaller, and real.

23.3 Formation of Images by Spherical Mirrors

If an object is inside the focal point, its image will be upright, larger, and virtual.

Convex Mirrors

•  A Convex Mirror has no Focal point.

•  Hence it Cannot form a Real image

•  Virtual Images only.

• All the mathematical rules for mirrors still apply.

•  For a convex mirror, the image is always upright, and smaller.

•  Convex mirrors can compress a large view into a small image. •  Often used to provide a view of a whole room, or a street.

23.3 Formation of Images by Spherical Mirrors

Problem Solving: Spherical Mirrors 1.  Draw a ray diagram; the image is where the rays

intersect.

2.  Apply the mirror and magnification equations.

3.  Sign conventions: if the object, image, or focal point is on the reflective side of the mirror, its distance is positive, and negative otherwise. Magnification is positive if image is upright, negative otherwise.

4.  Check that your solution agrees with the ray diagram.

Example Calculation: Meatloaf vs Toyota/Ford etc…..

“Objects in the mirror are closer than they appear”

“Objects in the rearview mirror may appear closer than they are.”