Light and geometrical optics

Question 1

What are the particulate and wavy aspects of light?

Answer 1

Particulate: Photons (packet of energy)

Wavy: Light interference and diffraction (bending at two different media)

Question 2

What is an electromagnetic field?

What is polarized light?

Answer 2

A field which has two perpendicular vectors at every point, the electric field vector (E) and the magnetic induction field vector (B)

The electromagnetic wave front is polarized in a straight line when E and B are fixed at all times. Thus polarized light is light that has waves in only one plane.

Question 3

What is ‘reflection?’

Define the incident ray

Answer 3

The process by which light rays bounce back into a medium from a surface with another medium (versus being refracted or absorbed)

The incident ray is the ray that arrives, the one that bounces back is the ‘reflected’ ray

Question 4

What are the laws of reflection? (2)

Answer 4

1. The angle of incidence (I) equals the angle of reflection (R) at the normal (N, the line perpendicular to the surface)
2. The I, R and N all lie in the same plane

Question 5

Contrast virtual and real images

Answer 5

Virtual: A reflected image that has no light rays passing through it and cannot be projected upon a screen

Real: A reflected image that has light rays passing through it and can be projected on a screen

Question 6

Describe reflected images in plane surface mirrors

Answer 6

• Virtual
• Erect
• left-right inversed
• Distance conserved (distance of image from plane has same magnitude, but opposite sign as real distance)

Question 7

How is light focused for non-plane mirrors?

Answer 7

Convex mirror
- Diverges light

Convex lens
- Converges light

Concave mirror
- Converges light

Concave lens
- Diverges light

Question 8

Define the following terminology for spherical mirrors:

• Radius of curvature (r)
• Centre of curvature (C)
• Focal point (F)
• Vertex
• axis
• focal length
• image distance (i)
• Object distance (o)
• Linear aperture (AB)

Answer 8

• Radius of curvature (r),
• Centre of curvature (C)
• Focal point (F)
• Vertex (centre of mirror)
• axis (line through C and V)
• focal length (distance from F to V)
• image distance (i) (distance from V to image along axis)
• Object distance (o) (distance from V to object along axis)
• Linear aperture (AB) (cord connecting the ends of the mirror, the larger the aperture, the better the resolution

Question 9

With concave mirrors and convex lenses, where is the incident light?

What quality of the mirror/lens will produce image inversion? And what will affect image size?

Answer 9

Converged toward the axis.

focal length
0 < f (virtual and erect)
0 > f (real and inverted)
0 = f (formed for mirror, not formed for lens)

radius of curvature
0 < r (enlarged)
0 > r (reduced in size)
0 = r (same size as object)

Question 10

How are images formed for a convex mirror?

Answer 10

Always virtual, erect and smaller than the object.

Question 11

How are the relations between objects and image in concave and convex mirror calculated? (3 formulas)

Answer 11

1/i + 1/o = 1/f

f = focal length
i = distance from image
o = distance from object

f = r/2

M = magnification = -i/o

Question 12

What type of reflected images are being produced when i and o (distances from vertex to image/object) are positive/negative?

Answer 12

Positive: real
Negative: Virtual

this is the same for lenses

Question 13

What type of reflected images are being produced when r and f (radius of curvature and focal length) are positive/negative?

Answer 13

Positive: converging
Negative: diverging

same for lenses

Question 14

What type of reflected image is being produced when magnification (M) is positive/negative?

Answer 14

Positive: erect
Negative: inverted

same for lenses

Question 15

What values of M indicated an enlarged image? Diminished image?

Answer 15

Enlarged: more than 1

Diminished: less than 1

Question 16

What causes refraction?

Answer 16

The different speeds of light in the two media that a light is passing through.

Question 17

How do longer wavelengths travel in a medium (compared to shorter wavelengths)? What is the consequence of this for refraction?

Answer 17

Longer wavelengths travel faster in a medium than shorter wavelengths

Longer wavelengths are more susceptible to refraction, leading to dispersion (separation of white light into individual colours by differential refraction)

Question 18

What are the laws of refraction? (2)

Answer 18

1. The incident ray, the refracted ray and the normal ray all lie in the same plane
2. The path of the ray (incident and refracted parts) is reversible.

Question 19

When light passes from a more optically dense (higher n) medium into a less optically dense medium, what is the angle of refraction (θ2)?

Answer 19

There exists an angle of incidence that produces an angle of refraction of 90 degrees

This special angle of incidence is called the critical angle θc

This is because when the angle of incidence is less than θc, refraction occurs. If the angle of incidence is equal to θc, then neither refraction nor reflection occur.

Question 20

What happens when an angle of incidence is larger than the critical angle of incidence?

Answer 20

Total internal reflection occurs (the ray is reflected back into the more optically dense medium)

The θc (critical angle) is found in Snell’s law.

Question 21

How do convex lenses and concave lenses refract light?

Answer 21

Convex (fat in middle): converging lens, refracts towards the axis

Concave (thin in middle)`: diverging lens, refracts light away from the axis

Question 22

What are the paths that rays can travel through a lens? (3)

Answer 22

1. Incident ray parallel to the axis refracts through the focal point of the converging lens and comes from the focal point of a diverging lens
2. An incident ray through the focal point of a converging lens, or through the focal point of a diverging lens, are refracted parallel to the axis
3. Incident rays through the vertex are deviated (refracted)

Question 23

How are images for diverging lenses?

Answer 23

Always:

• Virtual
• Erect
• Reduced in size

(same for a convex mirror)

Question 24

What ar diopters (D)?

How are diopters difference for converging/diverging lenses?

Answer 24

D = 1/f

Where f is in metres. D is the refractive power of the lens, the larger the diopters, the stronger the lens. The diopters has a positive value for a converging lens and a negative value for a diverging lens.

Question 25

A glass fiber carries a light digital signal long distances with a minimum loss of amplitude. What optical property of glass allows this phenomenon?

Answer 25

Reflection

Light can be carried along a distance within a transparent material by means of ‘total internal reflection.’

Question 26

How do polarized glasses allow you to see plane polarized light (such as light reflecting from the hot layer of air on a desert road)?

Answer 26

They allow light in one plane (eg. vertical, horizontal or anywhere inbetween) to pass through the lens and become visible but absorb the other planes of light.

This is only true for transverse waves (such as light waves)

Question 27

How would one calculate the velocity of light if one wanted to (in a given medium)?

Answer 27

V = c/n

Where c is the speed of light in a vacuum and n is the index of refraction. Some common indexes of refraction are:

Vacuum: 1
Air: about 1
Water: 1.3
Glass: 1.5

None of this has to be memorized, just realize that n is always above 1, and therefore light velocity is slower in any material compared to in a vacuum.

Question 28

Refraction is dependent on the speed of light as it travels through a material (ONLY the material determines the speed). The angle of refraction is always measured relative to the normal (line perpendicular to the surface). Does a slower medium produce a smaller angle against the normal compared to the incident light beam, or a larger one?

Answer 28

When light is refracted by a material that slows light down (eg. glass), the angle of refraction is smaller than the initial incidence angle.

Question 29

Describe the critical angle of refraction? What happens when there is a larger angle of incidence?

Answer 29

This is the incidence of light angle that produces a refracted beam at exactly 90 degrees away from the normal (aka, parallel with surface of medium).

When the angle of incidence is larger than the critical angle, the beam of light is reflected back into the medium. this is called total internal reflection.

Question 30

When a wave travels from one medium to another and the velocity of the wave changes, what property of the wave is changing to produce a change in velocity?

Answer 30

Wavelength is changing, NOT frequency!

Question 31

If you get a negative sign for the distance of an image from a lens, what does this say about the image?

When calculating magnification, and the distance of the image is negative, but the distance of the object is positive, what must you do?

Answer 31

Negative image distance indicates that the image is being projected on the same side as the object (virtual image). This is how a magnifying glass (convex/converging lens) works.

When calculating magnification, you must assign a negative or positive value, depending on whether the image is upright (positive) or inverted (negative magnification).

Question 32

It is a general rule that if only one lens or mirror is involved in a problem, then the image is either both real/virtual and upright/inverted (which pairs go together?)

Answer 32

It is a general rule that if only one lens or mirror is involved in a problem, then the image is either both real and inverted OR virtual and upright

Question 33

Why do different colours refract slightly differently from a prism?

Answer 33

The index of refraction changes every so slightly for different wavelengths of colour, producing different angles of refraction for each wavelength of colour.

This is called a chromatic aberration in real lenses (which deviate from so-called ideal lenses, which are what we usually base our calculation/diagrams off of in this exam)

Question 34

The lens is about 2 cm from the retina. What is the focal length of the lens/cornea (two lenses in contact) to focus on a n object 20 cm away?

Answer 34

1/f = 1/o + 1/i

1/f = 1/20 + 1/2

1/f = 11/20

f = 20/11

f = 1.8

Question 35

Which of the following is true of the image formed on the retina?

I. It is real
II. It is inverted
III. It is reduced

Answer 35

All three!

The image formed on the retina is formed by a converging (convex) lens.

This means it is real, inverted and reduced.

Question 36

As the power input to a light bulb decreases, the brightness decreases. How doe the color of the emitted light change? Why?

Answer 36

The emitted spectrum shifts to longer wavelengths.

Smaller power used by the light bulb means less heating of the light bulb filament, and thus the filament will be cooler and emit light of smaller energy.

E = hc/λ

Longer wavelength will result in a smaller frequency and smaller energy. The wavelength emitted must shift to longer values to result in lesser energy.

Question 37

Visible light travels more slowly through an optically dense medium than through a vacuum.

What is the best explanation for this?

Answer 37

The light is absorbed and re-emitted by the atomic “structure” (not nucleus!).