23.4 Images Formed by 23.4 Images Formed by RefractionRefraction Rays originate from Rays originate from

the object point (the object point (O O ) ) and pass through the and pass through the image point (image point (II))

When When nn22 > > nn11,,

Real images are Real images are formed on the side formed on the side opposite from the opposite from the objectobject

pn

qn

h

h'M

2

1

p, q, and R are positive

23.5 Atmospheric 23.5 Atmospheric RefractionRefraction

There are many interesting There are many interesting results of refraction in the results of refraction in the atmosphereatmosphereSunsetsSunsetsMiragesMirages

Atmospheric Refraction Atmospheric Refraction and Sunsetsand Sunsets Light rays from the sun Light rays from the sun

are bent as they pass are bent as they pass into the atmosphere into the atmosphere

It is a gradual bend It is a gradual bend because the light passes because the light passes through layers of the through layers of the atmosphere atmosphere Each layer has a Each layer has a

slightly different index slightly different index of refractionof refraction

The Sun is seen to be The Sun is seen to be above the horizon even above the horizon even after it has fallen below itafter it has fallen below it

Atmospheric Refraction Atmospheric Refraction and Miragesand Mirages A mirage can be A mirage can be

observed when the observed when the air above the ground air above the ground is warmer than the air is warmer than the air at higher elevationsat higher elevations

The rays in path B are The rays in path B are directed toward the directed toward the ground and then bent ground and then bent by refractionby refraction

The observer sees The observer sees both an upright and both an upright and an inverted imagean inverted image

23.6 Thin Lenses23.6 Thin Lenses A thin lens consists of a piece of A thin lens consists of a piece of

glass or plastic, ground so that glass or plastic, ground so that each of its two refracting surfaces each of its two refracting surfaces is a segment of either a sphere or is a segment of either a sphere or a planea plane

Lenses are commonly used to Lenses are commonly used to form images by refraction in form images by refraction in optical instruments (cameras, optical instruments (cameras, telescopes, etc.)telescopes, etc.)

Thin Lens ShapesThin Lens Shapes

These are These are examples of examples of convergingconverging lenses lenses

They have They have positive focal positive focal lengthslengths

They are thickest They are thickest in the middlein the middle

More Thin Lens ShapesMore Thin Lens Shapes

These are These are examples of examples of divergingdiverging lenses lenses

They have They have negative focal negative focal lengthslengths

They are thickest They are thickest at the edgesat the edges

Focal Length of LensesFocal Length of Lenses The focal length, ƒ, is the image distance The focal length, ƒ, is the image distance

that corresponds to an infinite object that corresponds to an infinite object distancedistance This is the same as for mirrorsThis is the same as for mirrors

A thin lens has two focal points, A thin lens has two focal points, corresponding to parallel rays from the corresponding to parallel rays from the left and from the rightleft and from the right A thin lens is one in which the thickness of the A thin lens is one in which the thickness of the

lens is negligible in comparison with the focal lens is negligible in comparison with the focal lengthlength

Focal Length of a Focal Length of a Converging LensConverging Lens

The The parallel raysparallel rays pass through the lens and pass through the lens and converge converge at the focal point at the focal point FF

The parallel rays can come from the left or right The parallel rays can come from the left or right of the lensof the lens

ff is positive is positive

Focal Length of a Focal Length of a Diverging LensDiverging Lens

The The parallel rays divergeparallel rays diverge after passing after passing through the diverging lensthrough the diverging lens

The focal point is the point where the rays The focal point is the point where the rays appear to have originatedappear to have originated

ff is negative is negative

Ray Diagrams for Thin Ray Diagrams for Thin LensesLenses

Ray diagrams are essential for understanding Ray diagrams are essential for understanding the overall image formationthe overall image formation

Three rays are drawnThree rays are drawn The The first ray first ray is drawnis drawn parallel parallel to the first principle to the first principle

axis and then passes axis and then passes throughthrough (or appears to come (or appears to come from) from) one of the focal pointsone of the focal points

The The second raysecond ray is drawn is drawn through the center of the through the center of the lenslens and and continues in a straight linecontinues in a straight line

The third ray is drawn from the other focal point and The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axisemerges from the lens parallel to the principle axis

There are an infinite number of rays, these are There are an infinite number of rays, these are the convenient onesthe convenient ones

Ray Diagram for Ray Diagram for Converging Lens, Converging Lens, pp > > ff

The image is realThe image is real The image is invertedThe image is inverted

Ray Diagram for Ray Diagram for Converging Lens, Converging Lens, pp < < ff

The image is virtualThe image is virtual The image is uprightThe image is upright

Ray Diagram for Diverging Ray Diagram for Diverging LensLens

The image is virtualThe image is virtual The image is uprightThe image is upright

(b)(b)