# 25.5 Dispersion: the rainbow and prisms  (Page 2/4)

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Index of refraction n In selected media at various wavelengths
Medium Red (660 nm) Orange (610 nm) Yellow (580 nm) Green (550 nm) Blue (470 nm) Violet (410 nm)
Water 1.331 1.332 1.333 1.335 1.338 1.342
Diamond 2.410 2.415 2.417 2.426 2.444 2.458
Glass, crown 1.512 1.514 1.518 1.519 1.524 1.530
Glass, flint 1.662 1.665 1.667 1.674 1.684 1.698
Polystyrene 1.488 1.490 1.492 1.493 1.499 1.506
Quartz, fused 1.455 1.456 1.458 1.459 1.462 1.468

Rainbows are produced by a combination of refraction and reflection. You may have noticed that you see a rainbow only when you look away from the sun. Light enters a drop of water and is reflected from the back of the drop, as shown in [link] . The light is refracted both as it enters and as it leaves the drop. Since the index of refraction of water varies with wavelength, the light is dispersed, and a rainbow is observed, as shown in [link] (a). (There is no dispersion caused by reflection at the back surface, since the law of reflection does not depend on wavelength.) The actual rainbow of colors seen by an observer depends on the myriad of rays being refracted and reflected toward the observer’s eyes from numerous drops of water. The effect is most spectacular when the background is dark, as in stormy weather, but can also be observed in waterfalls and lawn sprinklers. The arc of a rainbow comes from the need to be looking at a specific angle relative to the direction of the sun, as illustrated in [link] (b). (If there are two reflections of light within the water drop, another “secondary” rainbow is produced. This rare event produces an arc that lies above the primary rainbow arc—see [link] (c).)

## Rainbows

Rainbows are produced by a combination of refraction and reflection.

Dispersion may produce beautiful rainbows, but it can cause problems in optical systems. White light used to transmit messages in a fiber is dispersed, spreading out in time and eventually overlapping with other messages. Since a laser produces a nearly pure wavelength, its light experiences little dispersion, an advantage over white light for transmission of information. In contrast, dispersion of electromagnetic waves coming to us from outer space can be used to determine the amount of matter they pass through. As with many phenomena, dispersion can be useful or a nuisance, depending on the situation and our human goals.

## Phet explorations: geometric optics

How does a lens form an image? See how light rays are refracted by a lens. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen.

## Section summary

• The spreading of white light into its full spectrum of wavelengths is called dispersion.
• Rainbows are produced by a combination of refraction and reflection and involve the dispersion of sunlight into a continuous distribution of colors.
• Dispersion produces beautiful rainbows but also causes problems in certain optical systems.

## Problems&Exercises

(a) What is the ratio of the speed of red light to violet light in diamond, based on [link] ? (b) What is this ratio in polystyrene? (c) Which is more dispersive?

A beam of white light goes from air into water at an incident angle of $\text{75}\text{.}0º$ . At what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?

$\text{46}\text{.}5º\text{, red; 46}\text{.}0º\text{, violet}$

By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?

(a) A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a $\text{30}\text{.}0º$ incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?

(a) $0\text{.}\text{043º}$

(b) $1\text{.}\text{33 m}$

A parallel beam of light containing orange (610 nm) and violet (410 nm) wavelengths goes from fused quartz to water, striking the surface between them at a $\text{60}\text{.}0º$ incident angle. What is the angle between the two colors in water?

A ray of 610 nm light goes from air into fused quartz at an incident angle of $\text{55}\text{.}0º$ . At what incident angle must 470 nm light enter flint glass to have the same angle of refraction?

$\text{71.3º}$

A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00 cm thick flat piece of crown glass and back to air again. The beam strikes at a $\text{30}\text{.}0º$ incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

A narrow beam of white light enters a prism made of crown glass at a $\text{45}\text{.}0º$ incident angle, as shown in [link] . At what angles, ${\theta }_{\text{R}}$ and ${\theta }_{\text{V}}$ , do the red (660 nm) and violet (410 nm) components of the light emerge from the prism?

$\text{53.5º}\text{, red;}$ $\text{55.2º}\text{, violet}$

Describe an experiment to determine short half life
what is science
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
what is physics
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
it is when you get up of your arse and do some real work 😁
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
what are the fundamentals qualities
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
your fat arse sitting all day is a good reference of three dimensional numbnut
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
you mean in three dimensions......numbnut
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
time seems to flow in one direction...but I the past present and future happen every moment time flies regardless.
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman
if v=ktx Ly Mz find the value of x,y and z
x=v=ktx Ly Mz find the value of x,y and z
y=v=ktx Ly Mz find the value of x,y and z
z=v=ktx Ly Mz find the value of x,y and z
now get your lazy arse up and clean the kitchen 😁
I want to join the conversation
😂
hmm
Stephen
what conversation you talking about? .....numbnut
how do i calculate for period of the oscillation
T=2π√(m÷k).K is spring constance
Ambe
T=2π√m/k
Lord
does the force in a system result in the energy transfer?
full meaning of GPS system
global positioning system
Noman
what's the use of the GPS
Matthew