Lenses

Combining prisms Combine a series of prisms and you can get an especially sharply focused image. A lens acts as a series of prisms.

Lenses allow us to manipulate light

Converging lenses: thicker across the middle focus light Diverging lenses thinner across the middle causes light to diverge

Anatomy of a lens Principal axis An imaginary line through the center of the imaginary sphere of which the lens is an imaginary slice Focal length The point through which light traveling parallel to the principal axis will converge Vertical axis

Light through a lens Ray parallel to the principal axis enters the lens. Travels from less optically dense medium to more optically dense medium: Light bends towards the normal

Light through a lens Ray traveling through the lens enters the air. More optically dense to less optically dense: Light bends away from the normal

Light converges on focal point Principal axis i ri r Rays passing through converging lens meet at focal point The distance from the center of the lens to the focal point is called the focal length.

Ray 1

Ray 2

Ray 3

Rays converge? It’s a real image! Images inverted.

Eyes Cow eyes are quite similar to human eyes.

Eyes The lens of a cow’s eye. Notice the image of the photographer is inverted.

Your brain is amazing. You see the world upside down… literally.

Anatomy of the eye Cornea: Protect the eye Refract light, n = 1.38 Iris: Sphincter Controls how much light enters eye Lens Refract light, n=1.40 Vitreous humor Fluid that gives eye its ~spherical shape Retina ~12 M rods detect intensity of light ~6 M cones detect color of light

Accommodation When the muscles around your eye relax, the lens is relatively thin. Images from far away are focused on your retina. When the muscles around your eye contract, the lens is relatively large. Images from nearby are focused on your retina. Read more. It’s very interesting!more

Moving an object closer to a convex lens Notice the behavior of the image as the distance between the object and lens decreases.

Summary for converging lenses Case 1 Case 2 Case 3 Case 5 Case 4 Five cases for object distances

More useful predictive model F’ F

More useful predictive model F’ F h0h0 hihi d0d0 didi

More useful predictive model F h0h0 hihi object image d0d0 didi

More useful predictive model F h0h0 hihi Lens to focal point Focal point to image

More useful predictive model

Thin Lens equation

Magnification

Diverging lenses? Rays pass through the lens, but are spread apart in the process; they diverge. The image appears upright and is not able to be projected.

Ray 1: from top of object parallel to principal axis, travels straight away from focal point Ray 2: from top of object through center of lens Virtual image forms where lines appear to intersect Ray diagram for diverging lens

Ray 1: from top of object parallel to principal axis, through focal point on opposite side. Ray 2: from top of object through center of lens, refracts parallel to principal axis Ray 3: from top of object through center of lens Virtual image forms where lines appear to intersect Objects inside the focal length of converging lens

The image from the first lens serves as the object for the second lens, the image of which can serve as the object for a third lens, etc. The magnification of the system is the product of the magnification of each separate lens. Multiple lenses

Quantified Gd o = 100 cm; f = 5.00 cm Ud i = ? E S S What is the position of an image of a 7.6-cm-high action figure placed 1.00 m in front of a camera lens with a 50.0 mm focal length? Try it first

Quantified Gd o = 100 cm; d i = 5.26 cm; h o = 7.6 cm Uh i = ? E S S What is the size of an image of a 7.6-cm-high action figure placed 1.00 m in front of a camera lens with a 50.0 mm focal length? Try it first

Summary of mathematical relationships