Lenses

Refraction• (p 308) Refraction occurs when a wave

changes the direction in which it is moving• This is caused by a change in speed as the

wave passes from one medium to another

• Similar to reflection, the angles of incidence and the angles of refraction are measured with respect to the normal

• (p308) the index of refraction the greater the greater the change in direction:

• Diamond: n = 2.42; ice: n = 1.31; air n = 1.00

• ( p 310) Snell’s Law:

• Question: what happens to the frequency of the waves or light when it passes from one medium to another?

• Answer: The frequency done not change

• (p 310) when light passes from a low index of refraction to a higher index of refraction, light slows down & bends toward the normal

•(add in margin) bending toward normal: from smaller “n” to a larger “n”

• (p 310) when light passes from a high index of refraction to a lower index of refraction, light speeds up & bends away from the normal•(add in margin) bending away from normal: from larger “n” to a smaller “n”

• (add to margin p 310)Example 1:

H2O

Air

Glass

air

Example 2: Example 3: (H2O drop)

Example 4: Example 5:white light rainbow

A ray on the normaldoes not bend

• Where would you have to aim the spear to catch the fish?

•(p 312) A pool of water is deeper than it appears because the light waves are sharter in water

Total internal reflection

• (add to p 313) total internal reflection only occurs when light rays are traveling from larger to smaller “n”

• The angle of incidence which results in a refracted angle of 90o is called the critical angle

Critical Angle Calculation • (add diagram to p315 #3) What is the critical

angle for air/lucite (n =1.51) interface?

• (p 312)The highway can appear to be wet. The wet road is a mirage. What is seen is a reflection of the sky on the hot road (or sand)

• The index of refraction of hot air is less that the index of refraction of cool air. Total reflection can occur-you see a reflection of the sky

• the twinkling of stars or distant lights is due to refraction. The direction of the light changes as it passes through the air at different temperatures

• You see an image of the sun for a few minutes before it rises and after it sets because the earth’s atmosphere refracts the light from the sun

Diagram:

Fiber Optics• (p 313) Fiber optics make use of total

internal reflection

• Fiber optics are replacing electric ciruits in communication technology

• Physicians use fiber optics to look inside your body

Refraction from Lenses• Lenses are a practical application of refraction• (p 326) there are 2 types of lenses:concave convex

•(p326)A convex lens is a converging lens: it brings light rays together

(Diagram p 327)

•(p 326) A concave lens is a diverging lens: it spreads out light rays

(Diagram p 327)

• (p 328) Because light can travel in either direction through a lens, we usually indicate a focal point on both sides of a lens

• A convex lens has a real focal point• A concave lens has a virtual focal point

•(add to margin p328)

concave convex

mirror f + f -

lens f - f +

Ray Diagram for Convex (Converging) Lenses

We will use the same rays as with mirrors

(p329a) Ray 1: parallel and through “f”

(p 330c) Ray 3:through “f” and then parallel

• (add p330)(remember rays pass through lenses but bounce off (reflect from) mirrors!)

• object outside “2f”: image inverted, smallerreal

• object at “2f’: image invertedsame sizereal

• Object between image inverted“2f” and “f” largerreal

• Object at “f” no image produced• Object inside “f” image erect

largervirtual

• The image is erect, larger and virtual

Ray Diagram for Convex Lens: object inside “f”

•We still follow the same pattern but we have to extend the refracted rays:

Ray Diagram for Diverging Lens

• (p 332) The image is erect, smaller, virtual

Chromatic Aberration (add to margin p333)

• Different wavelengths of light refracted by a lens focus at different points– Violet rays are refracted more

than red rays– The focal length for red light is

greater than the focal length for violet light

• Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses

Sign Conventions for lenses• (p332) the characteristics of images formed

by convex lenses are the same as those formed by concave mirrors

• the characteristics of images formed by concave lenses are the same as those formed by convex mirrors

• The sign conventions for mirror and lenses are the same: real +

virtual –erect +inverted -

Lens Formulae

• Lens equation:

• Magnification:

• (p 333/334)See example problems 1 & 2