nats 1311 - from the cosmos to earth our second exam will be next thursday, october 30 at the...

NATS 1311 - From the Cosmos to Earth

Our second exam will be next Thursday, October 30 at the regular class time. We will have a review Tuesday (Oct. 28) - at a time to be determined in class today - in the room next to where the regular lab is held. The exams will cover everything that we have covered in class up to the end of class Tuesday.


Lenses and Mirrors


Properties of Light

Law of Reflection - Angle of Incidence = Angle of reflection

Law of Refraction - Light beam is bent towards the normal when passing into a medium of higher Index of Refraction.

Light beam is bent away from the normal when passing into a medium of lower Index of Refraction.

Index of Refraction -

Inverse square law - Light intensity diminishes with square of distance from source.

€

n=Speedof lightin vacuumSpeedof lightin amedium

€


Normal

Law of Reflection

Angle of incidence () = angle of reflection ()

The normal is the ray path perpendicular to the mirror’s surface.


Center of curvature - the center of the circle of which the mirror represents a small arcPrincipal axis - a radius drawn to the mirror surface from the center of curvature of the mirror - normal to mirror surfaceFocus - the point where light rays parallel to principal axis converge; the focus is always found on the inner part of the "circle" of which the mirror is a small arc; the focus of a mirror is one-half the radiusVertex - the point where the mirror crosses the principal axisFocal length - the distance from the focus to the vertex of the mirror

Geometry of a Concave Mirror

Focus

Principal axisVertex

Focal length


Index of Refraction

As light passes from one medium (e.g., air) to another (e.g., glass, water, plexiglass, etc…), the speed of light changes. This causes to light to be “bent” or refracted. The amount of refraction is called the index of refraction.


Imagine that the axles of a car represent wave fronts. If the car crosses from a smooth to a rough surface at an angle, one tire of the axle will slow down first while the other continues at normal speed. With one tire traveling faster the other, the car will turn in the direction of the slow tire. This is how refraction works.

Refraction


AIR

GLASS / WATER

Slower Propagating Speed

Car

( Sand / Gravel )


AIR

GLASS / WATER


NORMAL


AIR

GLASS / WATER


NORMAL LIGHT BENDING TOWARDS THE

NORMAL

LIGHT RAY


n2

AIR

GLASS / WATER


NORMAL LIGHT BENDING TOWARDS THE

NORMAL

n1

Snell's Law

( Next Slide )


GLASS / WATER

Car

AIR


( Sand / Gravel )


AIR


GLASS / WATER

NORMAL

AGAIN, LIGHT BENDS TOWARDS THE NORMAL

upon entering a region with slower speed.

LIGHT RAY



GLASS /WATER

Car

AIR

( Sand / Gravel )


NOW LIGHT BENDS AWAY FROM THE NORMAL


GLASS /WATER

AIR

LIGHT RAY

NORMAL


Optical axis - axis normal to both sides of lens - light is not refracted along the optical axisFocus - the point where light rays parallel to optical axis converge; the focus is always found on the opposite side of the lens from the objectFocal length - the distance from the focus to the centerline of the lens

Geometry of a Converging (Convex) Lens

Optical axisFocus

Focal length


Fo

cal

Plan

el1 l2

o i

Geometry of a Simple Lens

€

1

o+

1

i=

1

f

M =−i

o=l2l1

f

Lens formula

Linear Magnification

Using the Gaussian form of the lens equation, a negative sign is used on the linear magnification equation as a reminder that all real images are inverted

The focal plane is where incoming light from one direction and distance (object distance o greater than focal length) is focused.


The image formed by a single lens is inverted.


Focal length

€

1

o+

1

i=

1

f

For astronomical distances, o ≅ ∞ and

1

i=

1

f or f = i

Fo

cal P

lane

NATS 1311 - From the Cosmos to EarthThe Eye

The eye consists of pupil that allows light into the eye - it controls the amount of light allowed in through the lens - acts like a simple glass lens which focuses the light on the retina - which consists of light sensitive cells that send signals to the brain via the optic nerve. An eye with perfect vision has its focus on the retina when the muscles controlling the shape of the lens are completely relaxed - when viewing an object far away - essentially at infinity.


When viewing an object not at infinity, the eye muscles contract and change the shape of the lens so that the focal plane is at the retina (in an eye with perfect vision). The image is inverted as with a single lens - the brain interprets the image and rights it.


Geometry is similar for a concave mirror - image is inverted.


Geometry of a Concave Mirror

Vertex

Focal length

€

1

o+

1

i=

1

f

For astronomical distances, o ≅ −∞ and

1

i=

1

f or f = i

Focal plane


Types of Optical Telescopes


Refracting Telescope

Uses lens to focus light from distant object - the eyepiece contains a small lens that brings the collected light to a focus and magnifies it for an observer looking through it.


The largest refracting telescope in the world is the at the University of Chicago’s Yerkes Observatory - it is 40 inches in diameter and 63 feet long.


Reflecting Telescope

The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.


Types of Reflecting Telescopes

Each design incorporates a small mirror just in front of the prime focus to reflect the light to a convenient location for viewing.


Mirror Position and Focus Animation

Focus Inversion Animation

The image from reflecting and refracting telescopes is inverted.

The focus is adjusted by changing the secondary mirror position.


The Keck Telescopes

Largest in the world - on Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.


The Hubble Space Telescope is 43.5 ft long and weighs 24,500 lbs. Its primary mirror is 2.4 m (7 ft 10.5 in) in diameter.

The Hubble Space Telescope

nats 1311 - from the cosmos to earth our second exam will be next thursday, october 30 at the...

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