Optics

The word optics, is come from Greek optikes, originally meant the study of the eye and vision. The term now refer to the study of all phenomena related to light. Geometrical optics is that branch which deals with reflection and refraction and the formation of images by optical instruments. It treats light as propagating in straight lines or rays.

Physical optics is the study and explanation of optical phenomena in term of the wave nature of light. This branch includes such phenomena as interference, deffraction, and polarization, as well as the subdivisions electrooptics, magetooptics, crystal optics and so on. Quantum optics has to do with the particle nature of light manifest in certain phenomena such as the photoelectric effect.

The science of optics has its roots burried in ancient times, in about 300 BC. Euclid wrote to treatise entitled optics and Catoptics in which he gave the correct law of refflection and applied the law to the study of plane and curved mirror. He also mentioned the phenomena of refraction, but the true mathematical law governing refraction was not discovered until 1621, by Willebrord Snell.

Concave and Convex Mirror

Concave Mirror
All the rays coming parallel to the main axis (O) will be reflected back through the focal point. Thus, the reflected rays will converge / intersect at one point that is the focal point.

Concave Mirror

From the figure shows that the reflected rays intersect at a single point (focus).

Convex Mirror
All the rays coming parallel to the major axis will be reflected as if through a focal point. Can be seen in the picture. If the light comes parallel to the main axis, then the string will be split of the reflection (wide).

Convex Mirror

From the image above we can see that the reflected beam widening / scatter.
Linear magnification of the curved mirrors

M = h’/h = -s’/s

Where:

M = magnification
h’ = shadow height
h= objects height
-s’ = shadow distance
s = object distance

The general formula curved mirrors

1/f = 1/s’ + 1/s

Where:
f = hot-spot/mirror focus
s’ = shadow distance
s = object distance

Wave Problem Solving

Problem 1.
A saxophone is playing a steady note of frequency 266 Hz. The temperature in the room is 25 oC. suppose that at some instant the varying pressure at your eardrum is at a maximum. How far away in meters is the next pressure maximum?

Solution:
The distance between the pressure maxima is an integer number of wavelength. Therefore the shortest distance is the wavelength. The speed of sound at 25 C is 346.33 m/s. Then we can find the wavelength:

L = v/f = 346.34/266 = 1.3 m

Problem 2.
(Inquiry into Physics-5th ed. Ostdiek,Bord) The quartz crystal used in an electric watch vibrates with frequency 32,768 Hz. What is the period of the crystals motion?

Solution:
By definition the frequency is the inverse period. Then the period is

 ζ = 1/f = 1/32768 = 3.05 x 10^-5 s = 30.5 μs

Problem 3.
A sound wave traveling at 350 m/s has a frequency of 500 Hz. What is its wavelength?

Solution:
The wavelength is related to the frequency and the speed by the following relation.

λ = vT = v/f = 350/500 = 0.7 m

Problem 4.
Estimate how far away a cicada can be heard if the lowest possible audible intensity of a sound it produces is 5 x 10-10 W/m2 and the power of the cicada's sound source is. 4 x 10-6 W

Solution:
We can estimate that the total power of the cicada's sound is distributed uniformly over the spherical surface of radius R. Then at distance R the intensity of the sound is

I = 4 x 10^-6/4πR²

The largest radius is achieved when the intensity is I = 5 x 10-10 W/m2 . Then

R²= 4 x 10^-6/4π x 10^-10 = 637 m²

Then R = 25 m

Problem 5.
Light of wavelength 497.0 nm appers to have a wavelength of 500.2 nm when it reaches eart from a distance star. find the velocity of the star if the speed of light is 300,000,000 m/s.

Solution:
In this problem we need to use the expression for the Doppler shift of the frequency of the wave for an observer moving relative to the source of the waves.. If the source of the light (wave) is moving with a speed v then the change in the frequency is

Δf = v/c x f_o
where c = 3 x 108 m/s is the speed of light. Since

f = c/λ

Then
Δf  = Δ c/λ = c Δλ/λ²
and

From this expression we can find the speed of the source

v = c Δλ/λ = 3 x 10⁸ x (500.2 - 497) x 10^-9/(497 x 10^-9 = 2 x 10⁶ m/s

Geology Time

One of the most important discoveries of modern science has been the age of the Earth and the vast length of time encompassed by its history. The scale of this history, in the millions and billions of years, is recognized as geologic time.

Most cultures incorporate some form of creation mythology, for example, the biblical Book of Genesis. In the mid 17th century an Irish churchman Bishop James Ussher added the years in the biblical genealogies and concluded that the Earth was created in 4004 BC. This idea persisted for a long while, although the 18th century French scientist Georges Louis Lectec, comte de Buffon reasoned that the Earth cooled from an originally molten body and that this have required at least 75,000 years.

Buffon had to recant, but development of the principle of uniformitarianism in the late 1700d snd early 1800s provided geologists with new grounds for arguing that the Earth is far older than anyone had imagine.

Similarly, in 1859, Charles Darwin recognized that millions of years were necessary for small evolutionary changes to accumulate and produce the variety of life we see today. Because they lacked definitive, precise data, however, 19th century geologiests could only guess at the age of the Earth. In the meantime, an accurate, relative geologic time scale had been developed, which placed the main events of geologic history in proper sequence.