Sight and Wave Phenomena

Option A

Cornea – a transparent membrane through which light enters

Pupil - an aperture through which light enters the eye’s lens

- the pupil can increase in size to adjust the intensity of light entering the eye.

Ciliary muscle – ligaments that control the curvature of the lens

Retina – located at the back of the eye

- light is focused by the lens on the retina where rods and cones convert the light into electrical signalsOptic nerve – transmits these electric signals to the brain

Fovea – an area of exceptionally acute vision

- each cone is connected to a different nerve fiber

Cones are concentrated at the center and rods are found primarily along the edges of the retina

Rods detect light, dark and grays.

Scotopic vision – used at night or in low light

rods are used

distinguishes shapes but not colors, little detailCones detect color and are only sensitive to bright light.

Photopic vision – used during the day, cones are mainly used, shaped and colors are distinguished

There are three types of cones, for short, medium and long wavelengths.

The lens of the eye is a converging lens which means it focuses the light at a point (focal point). It cannot focus on two objects at different distances at the same time.

Depth of vision

The range of distances that can be seen clearly.

Accomodation

The ability of the lens to change its shape to focus on different distances.

Near point

The closest point on which the human eye can focus without straining. About 25 cm but depends greatly on age.

Far point

The largest distance the eye can focus on without straining. Considered to be infinityfor a normal eye (a few meters)

Cones are sensitive to the primary colors: red, blue and green.

Secondary colors (cyan, magenta and yellow) are composed of the primary colors two at a time.

Color blindness – most common kind is the inability to distinguish between red and green.

Partial color blindness – one type of cone is not functioning and only those colors dependent on that cone cannot be distinguished.

Complete color blindness – two types of cone are not functional and no color can be distinguished.

Diffraction is the spreading out of a wave as it goes past an obstacle or through an aperture.

When the wavelength is small compared to the aperture the amount of diffraction is minimal.

Diffraction

= q l/bq is the angle to the first minimum (radians!)l is the wavelength of the light usedb is the size of the opening

A single slit of width 1.5 mm is illuminated with light of wavelength 500.0 nm. Find the angular width of the central maximum.

q = 39o

The ability to distinguish between two objects.

Because light diffracts, two distant stars that are close together may appear to be one object.

Resolution

The Rayleigh criterion

Two sources are just resolved if the central maximum of one source falls on the first minimum of the other.

UnresolvedJust resolved

Well resolved

Diffraction pattern due to a circular opening

= 1.22 q l/bUseful in optical devices where b is the diameter of the opening.

The camera of a spy satellite orbiting at 200 km has a diameter of 35 cm. What is the smallest distance this camera can resolve on the surface of the earth (assume a wavelength of 500 nm).

= 1.22 q l/bq= (1.22 x 5 x 10-7)/0.35

= 1.74 x 10–6 rad

S = R q = 2 x 107 x 1.74 x 10-6

= 0.34 m

The headlights of a car are 2 m apart. The pupil of the human eye has a diameter of about 2 mm. Suppose that light of wavelength 500 nm is being used. What is the maximum distance at which the two headlights are seen as distinct?

= 1.22 q l/b = 3 x 10–4

radR = s/ = 700 qm

Only light that is oriented on the same plane as the filter will pass through

Polarization

Polarization by reflection

When light reflects off a surface, the reflected ray is partially polarized (“glare”).

The degree to which it is polarized depends on the angle of incidence.

Brewster’s LawThe Brewster angle is the angle of incidence that will

create reflected light that is 100% polarized.

n = tan q

Calculate the Brewster angle for light incident on the surface of water (n = 1.33).

q= 53.1o

A polarizer is a material with a molecular structure that only allows a specific orientation to pass through.

An analyser is a polarizer that is used to determine if light is polarized.

The intensity (brightness) of light passing through an analyzer is dependent on the angle the polarizer makes with the orientation of the light.

I = Iocos2q

Calculate in terms of Io the intensity of light passing through an analyzer when q = 40o.

I = .6 Io

Graph of Intensity vs angle.

Doppler effect

• The frequency of a wave changes when the source of the waves is in motion or the observer is in motion

• Higher pitch when the source is approaching, lower pitch when the source is moving away

• Higher pitch when the observer is approaching, lower pitch when the observer is moving away

The frequency of a car’s horn is 200 Hz when the car is at rest. What frequency will be heard if the car is approaching the observer at 30 m/s? The speed of sound in air is 330 m/s

f = 220 Hz

Moving source

The frequency of a car’s horn is 200 Hz when the car is at rest. What frequency will be heard if an observer is approaching the car at 30 m/s? The speed of sound in air is 330 m/s

f = 218 Hz

Light from distant stars is also affected by the Doppler Effect.

Df = v/c fDf = change in freq f = emitted freq

v = speed of source c = speed of light

Hydrogen in a distant galaxy emits light of wavelength 658 nm. The light received on earth is measured to be 689 nm. Find the speed of the galaxy.

v = 1.4 x 10 7 m/s