Ch. 23: Mirrors and Lenses

the plane mirror

s=s’

-s=object distance (do)

-s’=image distance (di)

^same so no distortion

-treat objects as sources of light (light from room bounces off object and goes to your eye); light doesn’t converge at virtual image

concave vs convex mirror

-concave: curves away from object

-Convex: curves towards object; always creates a virtual image

real vs virtual image

-real image: where light converges, can put on a screen

-virtual image: were light could theoretically cross, can’t get an image on the screen

2 special rays for a concave mirror

-green line parallel of optical axis: reflects and goes through the focal point

-blue line through focal point: reflects and becomes parallel to the optical axis (reverse of green)

-optical axis: horizontal line center of mirror; plane of reflection: vertical line back of mirror

-real image: both rays converge

what happens if an object is inside the focal point of a concave mirror?

will be blurry/can’t read it anymore, NOT a real image anymore

take all measurements from the

plane of reflection

2 special rays for a convex mirror

-green parallel to optical axis: diverges from focal point

-blue aimed at focal point: parallel to optical axis

*rays never cross so no real image; virtual image smaller and right side up, same side as radius of curvature

-optical axis: horizontal line center of mirror; plane of reflection: vertical line back of mirror

*ex=car side or rearview mirror; safety mirrors at stores

mirror and lens equations

mirror and lens sign conventions

true or false: m and h’ always have the same sign? R of the curvature is always positive?

true! true!

converging vs diverging lenses

-The left lens, called a converging lens, causes parallel rays to refract toward the optical axis. Focal Length > 0 (*f>0, R>0; only produce real image)

-The right lens, called a diverging lens, refracts parallel rays away from the optical axis. Focal Length < 0 (*f<0, R<0; only produce virtual image)

*for both: 2 curved sides=focal point on each side, and focal points same distance left and right from plane of refraction

-converging lens=

-diverging lens=

-converging lens=double convex lens (*careful! bc converging mirror=concave)

-diverging lens=double concave lens (*careful! bc diverging mirror=convex)

converging lens situation 1

converging lens situation 2

converging lens situation 3

diverging lens situation 1

diverging lens situation 2

diverging lens situation 3

how would you create a graph for the mirror equation variables?

-1/s’ on y-axis; 1/s on x-axis; y-intercept=1/f

-relating to y=mx+b: y=1/s’, m=-1, x=1/s, and b=1/f

far point

-The farthest distance at which a relaxed eye (with perfect vision) can focus is called the eye’s far point (FP)

-The far point of a normal eye is very large/; that is, the eye can focus on objects extremely far away. We will approximate this distance to be infinity for simplicity.

*ex=eye chart across the room

*ciliary muscles change focal length of lens; most refraction from lens; focus light on retina, humor fluid does little refraction

near point

-The closest distance (on average) at which a perfect eye can focus, using maximum accommodation, is the eye’s near point (NP) = 25 cm.

*normal near point (NP)=infinity, far away object:s=infinity, 1/s=1/infinity=0

*closest can focus on something; ex=bring phone to phase

corrective lenses

-Corrective lenses are prescribed not by their focal length but by their refractive power

-The power of a lens is the inverse of its focal length in meters: P=1/f

-The SI unit of lens power is the diopter, abbreviated D, defined as 1 D = 1 m−1

• Thus, a lens with f = 50 cm = 0.50 m has power P = 2.0 D

*+=converging lens, -=diverging lens

hyperopia

-A person who is farsighted can see faraway objects clearly, but their near point is larger than 25 cm, often much larger, so they cannot focus on nearby objects.

*eye stretched long way so light not focused on retina

hyperopia correction

-With hyperopia, the eye needs assistance to focus the rays from a near object onto the closer than normal retina.

-This assistance is obtained by adding refractive power with a converging lens.

• f>0; P>0

-virtual image made at person’s personal NP >25cm

*so rays pulled down and cross over earlier; makes virtual image at place where can see with out lens

any corrective lens makes a….

virtual image

-so s’ is always negative!

myopia

-A person who is nearsighted can clearly see nearby objects, but no amount of relaxation allows them to see distant objects

-Nearsightedness is caused by an eyeball that is too long

-Rays from a distant object come to a focus in front of the retina and have begun to diverge by the time they reach the retina.

*more common; converges before retina then spreads out

myopia correction

-To correct myopia, we needed a diverging lens to slightly defocus the rays and move the image point back to the retina

• f<0, P<0

*spread rays out so converge on retina

summary hyperopia vs myopia

-hyperopia=farsigthed, need converging corrective lens (f>0,P>0), virtual image made at person’s personal NP >25cm

-myopia=nearsigthed, need diverging corrective lens (f<0,P<0)