11. Geometrical Optics

Question 1

What is the speed of light? How is related to frequency and wave-length?

Answer 1

c = 3.0 x 10^8 m/s

if v = f x λ, then c = f x λ for light waves

Question 2

true or false, electromagnetic waves need a medium to travel similar to sound and waves of a rope.

Answer 2

FALSE, EMW’s do not need a medium (they can travel through a vacuum).

note that EM waves are transverse waves unlike sound waves (longitudinal)

Question 3

Explain the electromagnetic spectrum.

Answer 3

radio-waves, microwaves, infrared waves, ROYGBIV, UV, X-rays, gamma rays

large –> small λ

Question 4

t or f, energy of a wave is proportional to frequency.

Answer 4

True, thus gamma waves are highest energy while radio-waves are lowest.

Question 5

When electromagnetic radiation interacts with matter, energy can be absorbed or released in a quantized manner. This energy is called photons. What is the energy of a photon?

Answer 5

E = h x f
E = h x c / λ

h = Planck’s constant = 6 x 10^-34

Question 6

What is the wave-particle duality of light?

Answer 6

Light travels as a wave with its energy proportional to amplitude (squared)
Light interacts with matter as a particle, with its energy proportional to frequency

Thus, light acts as both a wave and a particle.

Question 7

What is the angle of incidence?

Answer 7

The angle between the normal (i.e. horizontal) and the incoming light.

The law of reflection states that the angle of incidence equals the angle of reflection

Question 8

What is the angle of refraction?

Answer 8

The angle between the refracted wave and the normal (i.e. the horizontal)

Question 9

A mediums index of refraction explains how much slower light will move passing through it (slower since light cannot exceed c). What is the formula for index of refraction?

Answer 9

Index of refraction (n) = c / v

v = the speed light travels in the new media
c = speed of light in a vacuum = 3 x 10^8

Question 10

compare light and sound traveling through media.

Answer 10

sound - requires media and travels fastest through solids slowest through gases
light - does NOT need media, travels slower when in any media.

Question 11

t or f, n = c / v, thus, the greater the value of n, the slower light travels for that particular medium.

Answer 11

true,

also, n can never be less than 1.

Question 12

What is Snell’s law (the law of refraction)?

Answer 12

n1 x sinϴ1 = n2 x sinϴ2

ϴ1 = angle of incidence
ϴ2 = angle of refraction

Question 13

Based on Snell’s law, n1 x sinϴ1 = n2 x sinϴ2 , if n2 > n1, then?

Answer 13

n1 x sinϴ1 = n2 x sinϴ2

if n2 > n1, then ϴ1 > ϴ2. Thus when light travels from a faster medium (n1) into a slower medium (n2), light bends towards the normal.

Similarly, if the n1 > n2, then ϴ2 > ϴ1, meaning when light travels from a slower medium into a faster one, light bends away from the normal.

Question 14

What is total internal reflection? When does it occur?

Answer 14

When light traveling in a higher refractive index approaches a medium of lower refractive index (e.g. light traveling in water towards the surface) it can be totally reflected (i.e. nothing is refracted).

This occurs when the angle of incidence exceeds the critical angle.

Question 15

How do you determine the critical angle for total internal reflection?

Answer 15

Sinϴ critical = n2 / n1

Question 16

t or false, at the critical angle, determined by Sinϴ critical = n2 / n1, light refracts along the surface of the water.

Answer 16

True, i.e. the angle of refraction is 90

Question 17

What is diffraction? What is dispersion?

Answer 17

diffraction - the distortion of light as it moves through a small slit. Diffraction is best seen when the slit is the same size as the lights wavelength.

dispersion - when light travels through a medium, frequencies actually travel at slightly different speeds (this does not occur in a vacuum). This slight difference can cause them to refract differently which is how you separate white light in a prism.

Question 18

What is plane-polarized light?

Answer 18

Typically, the electric fields oscillate in all directions (planes) as light moves. If the electric fields are restricted to moving in only one plane, this is polarized light.

Question 19

Curved mirrors, explain or draw the concepts of the center of curvature, radius of curvature, the focal point,, and focal length.

Answer 19

convex mirror: light —> (
concave mirror: light –> )

When light reflects off a concave mirror, it converges at the focal point. The focal point is located at half the distance of the center of curvature (C) which is the center of the circle if the curve continued. The distance from the mirror to C is the radius of curvature (r) and the distance from the mirror to the focal point is the focal length (f).

note that when light reflects off of a convex mirror the incident lights hypothetically continue and converge on the focal point behind the lens.

Question 20

How do you find the focal length of a curved mirror?

Answer 20

Recall that the focal point is at 1/2 the radius of curvature.

f = 1/2r

Question 21

t or f, for all mirrors, objects placed distant from the mirror will have their image converge at the focal point.

Answer 21

true, since the light off the object is all parallel to the mirror.

Question 22

Concave mirrors: What occurs when the object is close to the mirror but still further than f? What occurs if its closer than f?

What about for a convex mirror?

Answer 22

Distant objects: image converges at f.

close: image converges just beyond f.

closer than f: The light rays do not converge and the image is formed behind the mirror (similar to a convex mirror).

A convex mirror, the image always appears behind the mirror.
drawing it helps.

Question 23

What is a real image and a virtual image?

Answer 23

real image - light rays physically converge to form it Concave mirrors for objects further than f.

virtual image - light rays do not actually converge. Convex mirrors and concave mirrors for objects closer than f.

Question 24

What is the mirror equation?

Answer 24

1 /f = 1 / o + 1 / i

f = focal length
o = objects distance from the mirror 
i = the images distance from the mirror

f and i are positive when they are on the same side as the human observer (for mirrors, the same side as the object). They are negative if not.

Question 25

What is the equation for the magnification of an object?

Answer 25

m = - i / o

If m is positive (for mirrors, when its a convex lens), the image is upright.
If m is negative (for mirrors, when its a concave lens), the image is inverted.

real images are inverted
virtual images are upright

Question 26

What is the sign of f and i for a concave mirror?

Answer 26

For a concave mirror, the light is converged on the same side as the observer. Thus, f is positive and i is positive, .

*unless the object is within the focal length of the mirror in which case it acts convex-like.

Question 27

What kind of images do plane mirrors form?

Answer 27

Plane mirrors form virtual images. All virtual images are upright (real = inverted). Plane mirrors provide no magnification either.

Question 28

What is the significance of m being positive and negative?

Answer 28

m is positive = image is upright (which indicates that it is virtual)
m is negative = image is inverted (which indicates that it is real)

real images formed by concave mirrors
virtual images formed by convex mirrors and concave mirrors when o < f.

Question 29

Lens form images by refracting light. Explain the pathway of light for concave (diverging) and convex (converging) lenses.

Answer 29

A diverging lens (concave shape) refracts light so that it bends outwards.

A converging lens (convex shape like our eyes lens) refracts light so it bends inwards.

Question 30

t or f, most of what applies to mirrors, including the mirror equation, also applies to lenses.

Answer 30

true

Question 31

explain the focal length of lenses.

Answer 31

For a converging lens, light bends inwards and eventually physically crosses. Thus f is positive

For a diverging lens, light bends outwards and does not cross. Thus f is negative.

This contrasts mirrors.

Question 32

Just like mirrors, for lenses, real images are formed when the light converges on the same side as the observer. Explain f and i of concave and convex lenses.

Answer 32

concave (diverging) lens, light “converges” on the same side as the object. Thus the image is virtual (upright), f is negative and i is negative

convex (converging) lens, light converges on the same side as the observer. Thus the image is real (inverted), f is positive, i is positive.

Question 33

A lens with a short focal length must refract light (i.e. bend light) more aggressively than a lens with a longer focal length. What is the power of a lens?

Answer 33

Power = 1 / focal length.

longer the focal length, the less power.
f is measured in meters
power units = diopters (D)

note that the sign of f still matters. A diverging lens will have negative power.

Question 34

What is myopia and hyperopia?

Answer 34

myopia = nearsightedness. This means light converges before the retina. You need a diverging lens to correct this.

hyperopia = farsightedness. This means light converges after the retina. You need a converging lens to correct this.

Question 35

What is presbyopia and accommodation?

Answer 35

Lens accommodation is the process of your lens changing shape depending on what you are looking at. With age, this accommodation does not work as well and we get presbyopia.

We fix presbyopia the same way we fix hyperopia