Refraction and Lenses

refraction: the bending of light as it travels at an angle from one transparent medium into another less When light goes from a… dense medium more more to a… dense medium, less toward it bends… the normal. away from It has been found that light obeys the principle of least time.

angle of incidence, Qi normal incident ray refracted ray AIR (less dense) incident ray refracted ray Qi for 2nd boundary angle of refraction, Qr GLASS (more dense) AIR (less dense) Qr for 2nd boundary

“ZAP!” “LASER…” “Costing one MILLION dollars…” AIR (less dense) GLASS (more dense) “LASER…” AIR (less dense) “Costing one MILLION dollars…”

Index of Refraction n = index of refraction; c = 3.00 x 108 m/s; v = velocity of light in mat’l (m/s) In general... n > 1.000. Snell’s Law incident medium (ni) Qi refracting medium (nr) Qr

Light in air is incident on diamond (n = 2.419) at 43.0o. Find the angle of refraction. 43.0o n = 1.000 n = 2.419 Qr = 16.4o

Light in water is incident on cubic zirconia at 31.5o. Angle of refraction is 18.5o. Water’s index of refraction is 1.333. Find velocity of light in cubic zirconia. 31.5o n = 1.333 nr = nc.z. = ? 18.5o = 1.37 x 108 m/s

Examples of Refraction atmospheric refraction We continue to see the Sun after it has set. image actual path of light Earth object …n increases in lower atmosphere, so light bends more and more

Examples of Refraction (cont.) mirages object actual path of light image …not an optical illusion; can be photographed …“water” on road is an image of sky

Lenses Types of Lenses converging lenses diverging lenses double convex double concave plano-convex plano-concave concavo-convex convexo-concave

Lens Ray Diagrams First… 1. Draw a centerline vertically through lens. 2. Draw two F’s on the P.A. F F Rules: If ray comes in… then it is refracted… parallel to P.A. through F through lens’ center through F parallel to P.A. “NOT!”

real image: rays actually intersect; can project it on a screen virtual image: rays appear to intersect, but don’t; cannot project it on a screen p = object dist.  always on LEFT; always + q = image dist.  RIGHT,+,REAL; LEFT,–,VIRTUAL h = object height  always UPRIGHT; always + h’ = image height  UPRIGHT,+; INVERTED,– f = focal length CONVERGING,+ R = radius of curvature DIVERGING,–

q can be + (on right, real) Lens Equations Sign Conventions Converging Lens Diverging Lens f is + f is – q can be + (on right, real) or – (on left, virtual) q is always – (on left, virtual) h’ can be – (inverted) or + (upright) h’ is always + (upright) Thin Lens Equation and Magnification

Diverging lens has focal length 10.0 cm. A wiener-dog puppy 15.0 cm tall is 22.0 cm from lens. Describe image. (f = –10.0 cm; h = 15.0 cm; p = 22.0 cm) Diverging lens? “SUV.” = – 6.88 cm = 0.313  h’ = 0.313(15) = 4.70 cm SMALLER; UPRIGHT; VIRTUAL; on the left

Converging lens has focal length 7.7 cm. A 0.38 cm-tall real image of a thimble is formed 9.1 cm from lens. How far from lens is thimble? How tall is thimble? (f = +7.7 cm; h’ = –0.38 cm; q = +9.1 cm) = 50. cm –0.38 cm = –0.18 h = 2.1 cm

Correcting Vision with Lenses farsighted nearsighted What is in focus? cornea retina incoming rays from nearby objects incoming rays from distant objects

What is blurred? nearby objects distant objects How do we correct the condition? converging lens diverging lens

Total Internal Reflection Light traveling through water (n = 1.333) is incident on the water/air boundary at 48.606626o. Find angle of refraction. = 90.0o

The Critical Angle, Qc  the Qi for which Qr = 90o refracted rays normal (LESS dense medium) boundary Qc (MORE dense medium) reflected ray

total internal reflection -- light is incident from MORE dense medium to a LESS dense medium at Qi > Qc -- no light escapes from MORE dense medium e.g., T.I.R. in fiber optic cables light exiting light entering

Equation for the Critical Angle Find critical angle for light traveling from flint glass (n = 1.900) to crown glass (n = 1.522). = 53.23o crown glass flint

Dispersion  when polychromatic light is separated into its component ls -- occurs because different ls interact differently w/matter -- n differs for different ls -- By convention, the accepted index of refraction for a material is for l = 589 nm.

The various ls traveling through a lens focus at slightly different points; resulting blurring = chromatic aberration WHITE F F R 589 nm V -- reduced by... combining converging and diverging lenses made from different types of glass

h h