Lenses

Refraction of Light When light travels through a surface between

two different media, the light will be refracted if the angle of incidence is greater than zero.

If light is passing into a more dense media, it willbend towards the normal.

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n = =

Law of Refraction (Snell’s Law) The ratio of the sine of the angle of incidence to the

angle of refraction is a constant.n1 sin1 = n2 sin2

Where:n1, n2 = index of refraction 1 = Angle of incidence 2 = Angle of refraction

speed of light in a vacuum c speed of light in the material v

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Light Passing Through Glass

θ1

θ4

θ3θ2

IncidentRay

ReflectedRay

RefractedRay

Air AirGlass

Note: 1 = 4 2 = 3

Lenses and Their Uses Eyeglasses first made around the 13th

century. Galileo used them as a telescope to

discover the moons of Jupiter and the phases of Venus.

Other applications include microscopes, overhead projectors and cameras.

A special type of lens, called the fresnel lens, is used in lighthouses, traffic lights, rear windows of motor homes and overhead projectors.

Definition of a Lens What is a lens?

A lens is made of a transparent material such as glass or plastic such that the index of refraction is greater than that of air.

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Types of Thin Lenses What types of lenses are there?

Convex (Converging): A lens that is thicker in the middle than at the edges. Converging lenses cause incident parallel rays to converge at a point.

Concave (Diverging): A lens that is thinner in the middle than at the edges. Diverging lenses cause parallel rays of light to diverge when leaving the lens.

Fresnel: A lens comprised of rings of glass prisms positioned above and below a lamp to bend and concentrate light into a bright beam.

Converging and Diverging Thin Lenses Convex/Converging Lens:

Concave/Diverging Lens:

F2F F 2F

1

3

2

F F

12

3

Principle Axis

Focal point

Focal point

Image Formation by Converging Thin Lens

F2F F 2F

3

2

•An object placed more than 2X the focal distance before the lens will produce an inverted and smaller real image.

•This type of lens is similar to those used in cameras.

1

Principle Axis

Object

RealImage

Image Formation by Converging Thin Lens

F2F F 2F

3

2

1

•An object placed between F and 2F will produce an inverted and larger real image.

•This type of lens is similar to those used in projectors.

Principle Axis

Object

Real Image

Image Formation by Converging Thin Lens

F2F F 2F2

1Principle Axis

•An object placed between F and the lens will produce an upright and larger virtual image.

•This type of lens is similar to a magnifying lens.

VirtualImage

Object

Image Formation by Diverging Thin Lens

F F

12

3

•A diverging lens always produces a virtual image that is upright and smaller than the object.

•This type of lens is used in glasses to correct for myopia (near sighted).

VirtualImageObject

Image Formation for Converging and Diverging Thin Lenses• Image formation for diverging lenses.• Image formation for converging lenses.

The Thin Lens Equations1 1 1do di f

Where:do and di are the distances of the

object and image from the mirror, respectively.

f = focal length.

Image height, hi di

Object height, ho do

+ =

m = = -

Example 1

F2F F 2FPrinciple Axis

Object

Image

do di

hi

hi

f

1. An object is placed at a distance of 6 cm from a converging lens. The focal length of the lens is 2 cm. The distance of the image to the lens is:a. 1.0 cm b. 1.5 cm c. 3.0 cm d. 4.5 cm e. 6.0 cm

Example 2 & 32. An object is placed between the focal point and

twice the focal length of a converging lens. The image formed will be:a. real and upright b. real and invertedc. virtual and upright d. virtual and invertede. located at the focal length

3. An object is placed at a distance of 20 cm from a converging lens. The resulting image appears at a distance of 80 cm from the lens. The image is magnified by a factor of:a. 0.25 b. 4.0 c. 8.0 d. 12.0 e. 16.0

Sign Conventions for Thin Lenses Focal Length

f is positive for a converging lens. f is negative for a diverging lens.

Object Distance do is + if the object is to the left of the lens (real object). do is - if the object is to the right of the lens (virtual object).

Image Distance di is + for an image (real) formed to the right of the lens by a

real object to the left. di is – for an image (virtual) formed to the left of the lens by a

real object. Magnification

m is + for an image that is upright with respect to the object. m is – for an image that is inverted with respect to the object.

Key Ideas Snell’s Law / Law of Refraction: Light will bend

toward the normal when transitioning from a media with a low index of refraction (e.g. air) to a media with a higher index of refraction.

Paraxial light rays parallel to the principle axis of a converging lens will come to a point called the focus.

Paraxial light rays parallel to the principle axis of a diverging lens will appear to have originated from a point called the focus.

Diverging lenses always form virtual images.

Key Ideas The thin lens equation can be used to determine

the distance an image forms from a lens and is the same as that used for spherical mirrors.

Ray diagrams can be used to determine where images will form.