Lenses
Dec 18, 2015
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.
www.hyperphysics.phy-astr.gsu.edu
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
www.sol.sci.uop.edu
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.
www.physicsclassroom.comwww.physicsclassroom.com
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
1
2
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
1
2
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 Equations
1 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 2F
Principle 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 & 3
2. 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.