Characteristics of Lenses

Lens  Is a transparent object with at least one curved side that causes light to refract.  Have 2 sides  Either side could be plane, concave or convex.  We group them into two: converging lenses (where the light rays come together at a common point) and diverging (when light rays spread apart)  Is a transparent object with at least one curved side that causes light to refract.  Have 2 sides  Either side could be plane, concave or convex.  We group them into two: converging lenses (where the light rays come together at a common point) and diverging (when light rays spread apart)

Converging vs Diverging Converging lenses have one or two convex surfaces and are thicker in the centre than on the edges. Diverging lenses have one or two concave surfaces and are thicker at the edges than at the centre.

Converging Lenses  When rays enter a biconvex lens, they move from a fast medium to a slow medium and the rays will refract toward the normals.  This causes the rays to converge slightly.  When the light rays leave the second surface of the lens, they move from a slow medium to a fast medium and will refract away from the normals. Because of the direction of the normals at this surface, the rays continue to converge.  When rays enter a biconvex lens, they move from a fast medium to a slow medium and the rays will refract toward the normals.  This causes the rays to converge slightly.  When the light rays leave the second surface of the lens, they move from a slow medium to a fast medium and will refract away from the normals. Because of the direction of the normals at this surface, the rays continue to converge.

Converging Rays

Diverging Lenses  When you have a biconcave lens, the light rays refract at each surface of a biconcave lens.

You Try It!  Page 489 # 1-4

Focal Point and Length  The principal axis of a lens is a straight line that passes through the centre of the lens, normal to both surfaces.  When rays that are parallel to the principal axis pass through a converging lens, the rays intersect at a point called the focal point.  In a diverging lens, you have to trace the diverged rays backward in order to see them intersect at a point called the virtual focus.  The two focal points are the same distance from the centre of the lens.  The principal axis of a lens is a straight line that passes through the centre of the lens, normal to both surfaces.  When rays that are parallel to the principal axis pass through a converging lens, the rays intersect at a point called the focal point.  In a diverging lens, you have to trace the diverged rays backward in order to see them intersect at a point called the virtual focus.  The two focal points are the same distance from the centre of the lens.

 The position of the focal point for a lens depends on both the index of refraction of the lens material and the curvature.  Lenses with the same shape but higher index of refraction bend light rays more, making the focal point closer to the lens  Lenses with larger curvatures but the same index of refraction have the same effect.  The position of the focal point for a lens depends on both the index of refraction of the lens material and the curvature.  Lenses with the same shape but higher index of refraction bend light rays more, making the focal point closer to the lens  Lenses with larger curvatures but the same index of refraction have the same effect.

Thick and Thin Lenses  Remember that spherical aberration happens when light rays from an object hit a curved mirror from the principal axis and fail to form a clear image point.  Lenses produce spherical aberration too, but only in thick lenses  Remember that spherical aberration happens when light rays from an object hit a curved mirror from the principal axis and fail to form a clear image point.  Lenses produce spherical aberration too, but only in thick lenses

Chromatic Aberration  Rays that are farther away from the principal axis of a lens do not pass through the focal point.  The edges of lenses act as a prism, so they disperse light into colours.  Rays that are farther away from the principal axis of a lens do not pass through the focal point.  The edges of lenses act as a prism, so they disperse light into colours.

You Try It!!  P. 493 # 1-5, 8.

Images Formed by Lenses

Ray Diagrams  You can predict the location, orientation, size and type of the image using ray diagrams.  Once the focal point has been identified, three key rays chosen close to the principal axis can help locate the image.  You can predict the location, orientation, size and type of the image using ray diagrams.  Once the focal point has been identified, three key rays chosen close to the principal axis can help locate the image.

 The first ray that leaves an object parallel to the principal axis, will go through the focal point on the image side.  The second ray passes through the focal point on the object side will leave the other side parallel to the principal axis.  The third ray passes through the centre of the lens and goes straight through.  The first ray that leaves an object parallel to the principal axis, will go through the focal point on the image side.  The second ray passes through the focal point on the object side will leave the other side parallel to the principal axis.  The third ray passes through the centre of the lens and goes straight through.

You Try It!  Using Table 12.1 on P. 495, draw a ray diagram for a converging lens.

Image Characteristics in Converging Lenses  Converging lens images change characteristics depending on where they are located in relation to the focal point.  When the object is between the focal point and the converging lens:  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual:  Converging lens images change characteristics depending on where they are located in relation to the focal point.  When the object is between the focal point and the converging lens:  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual: farther upright larger virtual

 The object is between one and two focal lengths away from the converging lens.  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual:  The object is beyond two focal lengths away from the converging lens.  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual:  The object is between one and two focal lengths away from the converging lens.  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual:  The object is beyond two focal lengths away from the converging lens.  Farther away or closer:  Upright or Inverted:  Larger or smaller:  Real or virtual: larger farther closer inverted smaller real

Image characteristics in Diverging Lenses  The image is always  Upright  Virtual  Closer to the lens  Smaller than the object  Regardless of the location of the object.  As the object moves farther from the lens, the image becomes smaller.  The image is always  Upright  Virtual  Closer to the lens  Smaller than the object  Regardless of the location of the object.  As the object moves farther from the lens, the image becomes smaller.

Thin Lens and Magnification Equations  Thin Lens Equation: 1 = fd i d o  Magnification Equation: m = h i = -d i h o d o  These equations are used for converging lenses only.  Thin Lens Equation: 1 = fd i d o  Magnification Equation: m = h i = -d i h o d o  These equations are used for converging lenses only.

You Try It!  P. 500 # 1-4  P 501 # 1-7  P. 500 # 1-4  P 501 # 1-7

Telescopes  Galileo (famous astronomer) used a telescope with two lenses: one converging (objective lens) and one diverging lens (eye piece).  Ray diagrams for telescopes: look at page 503 in text for examples.  Galileo (famous astronomer) used a telescope with two lenses: one converging (objective lens) and one diverging lens (eye piece).  Ray diagrams for telescopes: look at page 503 in text for examples.

Human Eye  Cornea: refracts light before it enters the eye  Retina: a layer of cells that respond to light and initiate nerve response.

Focusing the eye  Our eye’s lens can change shape and refract light to different extents.  Ciliary muscles make the lens shorter and thicker.  Our eye’s lens can change shape and refract light to different extents.  Ciliary muscles make the lens shorter and thicker.

Myopia  Near-sightedness  Eyes cannot focus on things in distance.  The image will form in front of the retina so when the rays meet the retina, they are spreading out again.  Creates a blurry image  A diverging lens is used to correct this, so it spreads out the rays so the meet at on the retina again.  Near-sightedness  Eyes cannot focus on things in distance.  The image will form in front of the retina so when the rays meet the retina, they are spreading out again.  Creates a blurry image  A diverging lens is used to correct this, so it spreads out the rays so the meet at on the retina again.

Hyperopia  Far-sightedness  Cannot focus on objects close to the eye  Light rays reach the retina before they meet, making things blurry  Corrected with a converging lens so it bends the light closer together before they meet the cornea

Presbyopia  Presbyopia happens when a person ages their lenses become stiff and the ciliary muscles can no longer make the lenses change shape.  Not caused by length of the eyeball like hyperopia or myopia  Cannot focus on close objects  Use converging lenses to correct  If person already has myopia, they will need bifocals so they can see close and far.  Presbyopia happens when a person ages their lenses become stiff and the ciliary muscles can no longer make the lenses change shape.  Not caused by length of the eyeball like hyperopia or myopia  Cannot focus on close objects  Use converging lenses to correct  If person already has myopia, they will need bifocals so they can see close and far.

Astigmatism  Is caused by an incorrectly shaped cornea.  Produces blurry vision  Is caused by an incorrectly shaped cornea.  Produces blurry vision

You Try It!  P. 511 # 4, 5, 8