Book 3: Optics

Question 1

What are some facts about light?

Answer 1

Light is a form of energy that can travel in a vacuum. It travels at a very high speed at about 3*10^8 m s^-1. Light travels in straight lines.

Question 2

What are the kinds of light beams?

Answer 2

Parallel beam formed by parallel light rays, divergent beam formed by widening light rays, and convergent beam formed by narrowing light rays that cross at a point.

Question 3

What are luminous and non-luminous objects?

Answer 3

Luminous objects produce their own light, while non-luminous objects do not produce their own light, and are only visible when there is light shining on them.

Question 4

What are the shapes of the cone of rays from an object near, far, and very distant from us respectively?

Answer 4

near objects: divergent
far objects: less divergent
very distant objects: parallel

Question 5

What are the incident ray, the reflected ray, the normal, and angle of incidence, and the angle of reflection when a ray of light bounces of a plane mirror?

Answer 5

incident ray: the light ray that approaches the mirror
reflected ray: the light ray that leaves the mirror after reflection
normal: an imaginary line that is perpendicular to the mirror at the point where the incident ray hits the mirror
angle of incidence: the angle between the incident ray and the normal
angle of reflection: the angel between the reflected ray and the normal

Question 6

What are the laws of reflection?

Answer 6

The inident ray, the reflected ray, and the normal all lie on the same plane.
The angle of incidence is equal to the angle of reflection.

Question 7

What is regular reflection and diffuse reflection?

Answer 7

Reflection occurs when light hits a surface. If the surface is flat and smooth, the normals at different positions are parallel to each other. When parallel light rays fall on such a surface, the angles of incidence and reflection are all the same, and parallel rays and reflected in the same direction, resulting in regular reflection.
On the other hand, the normals at different points on a rough surface point at different directions. When parallel light rays fall on the surface, they are reflected towards different directions, resulting in diffuse reflection.

Question 8

What is a virtual image when light is reflected in a plane mirror?

Answer 8

The light rays reflected by the mirror appear to come from a point behind the mirror. Since the rays do not actually come from the image, and the image cannot be projected on a screen, it is called a virtual image.

Question 9

What are the relationships between the virtual image formed by a plane mirror and the real object?

Answer 9

The line joining the object and the image is perpendicularly bisected by the plane mirror.

Question 10

What is the orientation of the image in a plane mirror?

Answer 10

The image is behind the mirror, virtual, at the same perpendicular distance from the mirror as the object is, of the same size of the object, and erect but laterally inverted.

Question 11

What are the refracted ray and the angle of refraction?

Answer 11

refracted ray: the light ray that crosses the boundary after refraction
angle of refraction: the angle between the refracted ray and the normal

Question 12

What are the laws of refraction and what is the Snell’s law?

Answer 12

When a ray of light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant: sini/sinr=constant (Snell’s law), and the incident ray, the refracted ray, and the normal all lie in the same plane.
The Snell’s law can also be restated as n1 sina1=n2 sina2 with n being the refractive index.

Question 13

What is refractive index?

Answer 13

For the case when light travels from air to another medium, the constant ratio is called the refractive index of the medium. A medium with a larger refractive index is a optically denser medium, while a medium with a smaller refractive index is a optically less dense medium.

Question 14

What is the speed of light in different mediums?

Answer 14

The refractive index of a medium is directly proportional to the speed of light, and it equals the ratio of the speed of light in air to that in the medium.
n=c/v, where c is the speed of light in air and v is the speed of light in the medium.

Question 15

What is dispersion?

Answer 15

Dispersion is when white light passes through a prism and results in a colour spectrum consistng of red, orange, yellow, green, blue, indigo, and violet.

Question 16

What are some daily examples of refraction?

Answer 16

Objects appearing shallower in water: the apparent depth seen by the observer is shallower than the actual depth as light is refracted in water.
objects appearing broken in water
refraction in air: since hot air has a smaller refractive index than cold air, when we see an object through unstable hot air, it appears blurred and flickering. Air closer to the top of the atmosphere has a smaller refractive index, which causes refraction of the sun and the sun appearing to be higher.

Question 17

What are the conditions needed for total internal reflection?

Answer 17

light travels from an optically denser medium to an optically less dense medium, and that the angle of incidence i is larger than the critical angle c.

Question 18

How can the critical angle for total internal reflection be found?

Answer 18

n=1/sinC or C=sin^-1(1/n)

Question 19

What are examples of total internal reflection?

Answer 19

using prisms as mirrors: produces quality clear images
diamonds: their high refractive index causes them to easily sparkle when cut at the right facets
optical fibres: light enters the opltical fibre and after total internal reflections, it emerges from the other end, which is ideal for carrying light signals through long distances
mirage: an illusion where the observer sees a wet and reflective surface ahead, but is actually the total internal reflection of the image of the sky
fish-eye view: a diver underwater can see everything above the water surface squeezed into a cone

Question 20

What are convex and concave lens, and what are daily life examples of them?

Answer 20

Convex lens are lens that are thicker in the middle, while concave lens are lens that are thinner in the middle. An example of convex lens is a magnifying glass, and an example of concave lens is glasses.

Question 21

How do convex and concave lens bend light respectively?

Answer 21

A convex lens converge parallel light rays to a point and bends light inwards; therefore, it is called a converging lens. On the other hand, a concave lens diverge parallel light rays from a point and bends light outwards; therefore, it is called a diverging lens. However, when a light ray passes through the centre of any lens, it does not change its direction.

Question 22

What is the optical centre of a lens?

Answer 22

The centre of the lens; light passing through the optical centre experiences no directional change.

Question 23

What is the principal axis of a lens?

Answer 23

The principal axis is the line passing through the optical centre and perpendicular to the lens. Light rays parallel to the principal axis converge to the focus/appear to diverge from the focus.

Question 24

What is the principal focus of a lens?

Answer 24

The principal focus, denoted by F or F’, is the point that rays parallel to the principal axis converge to (for a convex lens) or appear to diverge from (for a concave lens) after passing through the lens.

Question 25

What is the focal length of a lens?

Answer 25

The focal length is the distance between the focus from the optical centre.

Question 26

What is the focal plane of a lens?

Answer 26

The focal plane is a plane passing through the principal focus and perpendicular to the principal axis. Parallel light rays that are not parallel to the principal axis converge to/appear to diverge from a point on the focal plane.

Question 27

What happens when a light ray passes through the optical centre of a lens?

Answer 27

When a light ray passes through the optical centre of a lens, there is no change in direction. However, there is a small lateral displacement between the incident ray and the emerging ray. For a thin lens, the lateral displacement is usually negligible.

Question 28

What are the factors contributing to the focal length of a lens?

Answer 28

curvature: a thicker lens has a shorter focal length.
material: a material with a greater refractive index/higher optical density usually has a shorter focal length.

Question 29

Which type(s) of image(s) can a convex lens form?

Answer 29

both real and virtual images: a real image is formed when the light rays from the object converge to a point after passing through the lens. Meanwhile, a virtual image is formed when the light rays from the object appear to diverge from a point after passing through the lens.
A real image can be captured on a screen but a virtual image cannot.

Question 30

What are the construction rules for a convex lens when drawing ray diagrams?

Answer 30

1. a light ray parallel to the principal axis is bent to pass through the principal focus on the other side of the lens.
2. a ray passing through the peincipal focus emerges parallel to the principal axis (converse of 1)
3. a ray passing through the optical cantre travels straight on. (in ray disgrams, lateral displacement is often considered negligible)

Question 31

How is a convex lens represented in ray diagrams?

Answer 31

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Question 32

What are general steps to drawing ray diagrams with convex lenses?

Answer 32

1. an arrow standing upright on the principal axis is usually drawn to represent the object.
2. draw two rays from the tip (usually one parallel to principal axis, and one passing through optical centre)
3. locate the intersection of the refracted rays as the position of the real image’s tip.
4. Draw the real image with a solid arrow with its tail on the principal axis.
5. If the refracted rays do not intersect, trace them back using dotted lines until a virtual image is located.
6. Draw the virtual image with a dotted arrow.

Question 33

What is the nature of the image when light rays from a distant object (at infinity; parallel light rays) pass through a convex lens?

Answer 33

The image lies on the focal plane. It is real, inverted, and diminished.

Question 34

What is the nature of the image when light rays from an object beyond 2F’ pass through a convex lens?

Answer 34

The image lies between F and 2F. It is real, inverted, and diminished.

Question 35

What is the nature of the image when light rays from an object at 2F’ pass through a convex lens?

Answer 35

The image lies at 2F. It is real, inverted, and has the same size as the object.

Question 36

What is the nature of the image when light rays from an object between F’ and 2F’ pass through a convex lens?

Answer 36

The image lies beyond 2F. It is real, inverted, and magnified.

Question 37

What is the nature of the image when light rays from an object at F’ pass through a convex lens?

Answer 37

The refracted rays are parallel, so there is no image formed.

Question 38

What is the nature of the image when light rays from an object within F’ pass through a convex lens?

Answer 38

The image is on the same side of the object. It is virtual, magnified, and erect.

Question 39

How are real and virtual images formed by a convex lens different in terms of properties?

Answer 39

For a convex lens, the nature of the image depends on the distance of the object from the lens. All real images formed by a convex lens are inverted and on the opposite side of the object, while all virtual images are erect and on the same side of then object.

Question 40

What are applications of convex lens?

Answer 40

Magnifying glass: a magnifying glass is a single conves lens. When magnifying the object, the object must be placed within F’ to produce a magnified, erect, and virtual image.
slide projector: the convex lens in a slide projector can produce a magnified image of the slide and project it onto a screen. For the projector to work peoperly, the slide must be placed at a position between F’ and 2F’.
camera: when the position of the convex lens inside a camera is well adjusted, the image of a distant objects can be formed on the film. The object should be put beyond 2F’.

Question 41

What type(s) of image(s) are formed by
a concave lens?

Answer 41

virtual image only: a concave lens can only form virtual images. Light rays from an object will always diverge after passing through the lens. They appear to come from the image, so our brains perceive it as though light comes from the image. However, since no light actually passes through the location of the image, the image is virtual.

Question 42

What are the construction rules for a concave lens in ray diagrams?

Answer 42

1. a ray parallel to the principal axis is bent so that it appears to come from the principal focus F’ on the same side.
2. a ray directed towards the principal focus F on the other side will emerge parallel to the principal axis (converse of 1)
3. a ray passing through the optical centre travels straight on (lateral displacement is often negligible)

Question 43

How is a concave lens represented in a ray diagram?

Answer 43

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Question 44

What are the general steps to drawing ray diagrams with concave lenses?

Answer 44

1. an arrow standing upright on the principal axis is usually drawn to represent the object.
2. draw two rays from the tip of the arrow (usually one parallel to the principal axis and one passing through the optical centre)
3. use dotted lines to extend the rays backward to locate the virtual image of the object’s tip.
4. draw a dotted arrow as the virtual image with its tail on the principal axis.

Question 45

What is the nature of the image when light rays from a distant object (at infinity; parallel light rays) pass through a concave lens?

Answer 45

The image lies on the focal plane. It is virtual, erect, and diminished.

Question 46

What is the nature of the image when light rays from an object between the lens and infinity pass through a concave lens?

Answer 46

The image lies within the focal length. It is virtual, erect, and diminished.

Question 47

What are the natures of images formed by concave lenses?

Answer 47

The image formed by a concave lens is always virtual, erect, diminished, and on the same side as the object.

Question 48

What are applications of concave lenses?

Answer 48

Concave lens can give a wider field of view. It is used in the peephole in a door or as a wide-angle lens on the rear window of a car.

Question 49

What is linear magnification?

Answer 49

Linear magnification = height of image/height of object = image size/object size = image distance/object distance.
A limear magnification m>1 implies that the image is magnified; m=1 implies no change in size; m<1 implies that the image is smaller.

Question 50

What type of lens is used if the image is dimished and erect?

Answer 50

concave lens

Question 51

What type of lens is used if the image is inverted?

Answer 51

convex lens (object between F’ and infinity)

Question 52

What type of lens is used if the image is erect and magnified?

Answer 52

convex lens (object within F’)

Question 53

What are factors affecting the brightness of images?

Answer 53

covered lens: when part of the lens is covered, a complete but dimmer image is formed. It is because some light rays from the object can still pass through the uncovered part of the lens. These light rays converge to form a complete image. However, since some light rays are blocked, the amount of light forming the image decreases. Therefore, the image becomes dimmer.
focal length: when the focal length is changed, the size of the image changes. When the same amount of light is distributed over an image, a smaller image is brighter than a larger image.

Question 54

What is the lens formula?

Answer 54

1/u+1/v = 1/f
(reciprocal of image distance + reciprocal of object distance = reciprocal of focal length)
object and image distances are positive when the image is real and vice versa. The focal length is positive when the lens is convex and vice versa.