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MONASH UNIVERSITY FOUNDATION YEAR

PHYSICS 2

CHAPTER 1: OPTICS

REVISION

1.1 Measurements and Units

Quantities that can be measured are called ______________ quantities. Examples of physical

quantities are like length, time, weight, current and many more.

Two things need to be mentioned while stating a physical quantity. First is the

______________value, second, is the ______________

According to the Systeme’ International (S.I.), seven physical quantities has been selected to be the

base quantity. The units for base quantities are called base units.

Each fundamental quantity in the metric system is defined in terms of a naturally-occurring

phenomenon, except for the mass standard.

Base Quantity Base Units

Name Symbol Name Symbol

Time

Length

Mass

Temperature

Electric current

Amount of substance

Luminous Intensity

Other physical quantities other than the base quantities are called the _________________. All

derived quantities are a combination of the base quantities.

Physical

Quantities

Defined as Unit Special Name

Density

Momentum

Force

Pressure

Work (Energy)

Power

Electrical Charge

Potential difference

Resistance

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1.2 Prefixes

For very large or very small numbers of quantities, we can use standard prefixes with the base

units.

Prefix Multiplying Factor Symbol

Pico

Nano

Micro

Mili

Centi

Deci

Kilo

Mega

Giga

Tera

Example

Energy stored in a bowl of ice cream = 12 000 000J

= 12 x 106

= 12 MJ

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1.3 Significant Figures

To count the number of significant figures, you must count up the total number of digits starting

at the first non zero digit, reading from the left to the right.

Fill in the blanks below

Always give your answers to the lowest significant figures found in the question.

A zero is said to be significant if:

(1) it is between two non-zero digits 3001 m (4 s.f), 30.001 m (5 s.f)

(2) it is at the end of a decimal expression 0.00310 km (3 s.f)

(3) it is required when expressing the number in scientific notation 3.10 x 106 m (3.s.f)

Otherwise a zero is considered to be only a placeholder. 150,000 m all four zeros are placeholders 1.5 x 10

5 m

0.0015 km all three zeros are placeholders 1.5 x 10-3

km

150. Gm no zeros are placeholders

(note the deliberate inclusion of the decimal) 1.50 x 1011

m

Example: A swimmer covers a distance of 100.0m in 68s. Calculate her average speed.

Scientific Notation.

Express your value so that it has one digit to the left of the decimal and all other significant digits to the

right of the decimal. It should then be multiplied by an appropriate power of 10.

(1) When the absolute value of the original number is greater than one, then moving the decimal point

will require the resulting number to be multiplied by 10 raised to a positive exponent.

(2) When the absolute value of the original number is less than one, then moving the decimal point will

require the resulting number to be multiplied by 10 raised to a negative exponent.

3 s.f 2 s.f 1 s.f.

4.62

0.00504

3.40 x 108

169

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OPTICS

Definitions

Luminous : An object that ______________ its own light is said to be luminous eg. Stars

Illuminated : An object becomes ______________t when light falls on it is said to be

illuminated.

Transparent : An object that ______________ light to pass through it is said to be transparent.

Eg Glass

Opaque : Objects that ______________ light/ do not allow light to pass through are called

opaque. Eg Wooden Shutters

Translucent : An object that allows light to pass through although you cannot see

______________ them eg ______________

Diffuse Reflection and Specular Reflection

a) Specular reflection

When parallel light is incident upon a

smooth surface (eg. Mirror) the reflected

rays are parallel to each other.

b) Diffused Reflection

When parallel light is incident upon a

rough surface, the reflected rays are in

various direction.

Light Ray and Light Beam

Light ray is a narrow band of light energy drawn as a straight line

Light beam is a collection of rays

Spectrum

A range of colours produced when white light is dispersed through a prism.

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Rectilinear Propagation of Light

The property of light traveling in straight lines.

Because of this, a few phenomena can be seen to happen.

i) Shadow- shadows mostly tell us about the nature of light. Light tends to travel in straight

lines and can be blocked by material objects. It doesn't bend around them and fill in the

area behind, at least at the scale we are considering here.

ii) Parallax is a displacement or difference in the apparent position of an object viewed along

two different lines of sight. Parallax creates ______________ through observed changes as you

move. Close one eye so that you are only looking through one lens. Hold out your thumb in

between you and another object, such as this Physics notes. There is some part of the notes that is

obscured by your thumb. However by moving your head, you can see around the thumb to the

pages. When your brain uses parallax, it gauges the relative movement of two objects as you

move, which will describe the relative distance between you and the two objects.

When an observer moves, the apparent relative motion of several stationary objects against a

background gives hints about their relative distance. If information about the direction and

velocity of movement is known, motion parallax can provide absolute depth information. This

effect can be seen clearly when driving in a car. Nearby things pass quickly, while far off objects

appear stationary.

A simple everyday example of parallax can be seen

in the dashboard of motor vehicles that use a needle-

style speedometer gauge. When viewed from directly

in front, the speed may show exactly 60; but when

viewed from the passenger seat the needle may

appear to show a slightly different speed, due to the

angle of viewing.

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iii) The discovery of the Pin-Hole Camera

A pinhole camera is the simplest camera possible. It consists of a light-proof box, some sort of

film and a pinhole. The pinhole is simply an extremely small hole like you would make with the

tip of a pin in a piece of thick aluminum foil.

A pinhole camera works on a simple principle.

Imagine you are inside a large, dark, room-

sized box containing a pinhole. Imagine that

outside the room is a friend with a flashlight,

and he is shining the flashlight at different

angles through the pinhole. When you look at

the wall opposite the pinhole, what you will

see is a small dot created by the flashlight's

beam shining through the pinhole. The small

dot will move as your friend moves his

flashlight. The smaller the pinhole (within

limits), the smaller and sharper the point of

light that the flashlight can creates.

Now imagine that you take your large, dark, pinhole-equipped room outside and you point it at a

nice landscape scene. When you look at the wall opposite the pinhole, what you will see is an

inverted and reversed image of the scene outside. Each point in the scene emits light, and, just

like the flashlight, the beam of light from that point passes through the pinhole and creates a point

of light on the back wall. All of the points in the scene do that at the same time, so an entire

image, in focus, is created on the back wall of the room. The image is very dim because the

pinhole is so small, but you can see it if the room is very dark.

A pinhole camera is simply a smaller version of that room, and the film inside the camera

replaces you. The film records the image that comes in through the pinhole. The camera records a

nice, in-focus image of the scene that you point the camera at. Usually, you have to expose the

film for a long time because the pinhole lets so little light through.

Let’s try to draw the path of light ray on the space below to show how pinhole camera works.

Why the image is inverted?

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Common Useful Cases which light interacts with matter

CCD (charge coupled device) and Photoelectric Cells

Photoelectric materials are light sensitive materials which releases an electron when light is shone on it.

Digital cameras and scanner make use of CCD to produce images from the environment. CCD is a large

scale integrated circuit which containing hundred to thousands of photosites (pixels). The CCD photosites

accomplish their task of sensing incoming light through the photoelectric effect and subsequently

emitting the signal that results in a digital image. The photoelectric material is able to produce an image

because of the fact that some colours reflect more light than the other. (i.e white reflects light while black

absorbs it)

Bleaching by UV Light

Bleaching materials/soap powder will have fluorescent components in it. When fluorescent components

are exposed to UV light, it will absorb the energy and emit bright light. That’s why most soap powder can

promise shining white clothes.

Photosensitive Cells in the Eye

The very back of the eye is lined with a layer called the retina which acts very much like the film of the

camera. The retina is a membrane containing photoreceptor nerve cells that lines the inside back wall of

the eye. The photoreceptor nerve cells of the retina change the light rays into electrical impulses and send

them through the optic nerve to the brain where an image is perceived.

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The Electromagnetic Spectrum

Characteristics of the Electromagnetic Spectrum

All electromagnetic radiation has fundamental properties and behaves in predictable ways according to

the basics of wave theory. Electromagnetic radiation consists of an ______________which varies in

magnitude in a direction perpendicular to the direction in which the radiation is traveling, and a

______________ oriented at right angles to the electrical field. Both these fields travel at the

______________ (c).

Ultraviolet (UV) - ____________________________radiation given off by electrical discharges,

such as sparks and lightning. It is also given out by stars such as our Sun. The

ozone layer in our atmosphere absorbs UV with wavelength less than 300nm but

its revent thinning increases the risk of skin cancers.

Visible light - ______________but other animals have eyes sensitive to different ranges. Eg.

Bees can see ultra violet.

Infra-red (IR) -is produced by all hot bodies. Common usage: ______________.

Radio Waves - can range from a wavelength of ______________. For mobile phones the

wavelength of radio waves used are about 1m. Radio waves less than 1m are used

for satellites, GPS, deep space probe whereas radio waves more than 1m is used

for radio and TV transmission.

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X-Rays - high energy waves which is dangerous to humans if they are exposed long term.

Gamma Rays - Gamma rays were discovered by P. Villiard in 1900. These are the most energetic

photons, apart from Cosmic rays. Thanks to their penetrative ability, gamma rays is

widely used in medicine. (eg radiotherapy- to divide cancerous cells etc.)

Dangers of being exposed to high energy waves (i.e the UV, X-rays and Gamma Rays)

Medical men have been aware for half a century that X rays can be destructive to human tissue.

Overdosage of X rays for benign purposes can have malignant consequences. Example: careless

treatment may cure acne, but cause skin cancer. Despite this established knowledge, X rays are still being

incautiously used as cure-alls. In the New England Journal of Medicine, Drs. Bradford Cannon, Judson

G. Randolph and Joseph E. Murray of Boston report that "patients continue to appear with permanent

tissue destruction that has resulted from relatively recent radiation treatment of acne, plantar wart,

eczema [and] superfluous hair." Examining 165 such cases from their personal files and the records of

Massachusetts General Hospital, the doctors starkly document the dangers of unnecessary exposure to

irradiation.

Items:

¶ Nearly half the patients suffered from persistent painful ulceration.

¶ Cancer appeared in 36—or 22%—of the cases.

¶ Of the ten patients who had been treated for acne, nine developed skin cancer.

"This appears to be an increasing problem," warn the doctors, "since twice the number were observed at

the Massachusetts General Hospital in the decade 1948 to 1957 as in the preceding decade." But the

worst may be yet to come. No one knows how many healthy people with histories of such treatment may

later develop malignancies. The interval for the appearance of cancer after treatment ranged in the study

from five to 55 years.

TIME Magazine

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The Law of Reflection

The Law of reflection states that the angle of incident, ______________ the angle of reflection .

These angles are measured with respect to the normal. The incident ray, reflected ray and the normal

is on the same plane.

Let’s try to draw ray diagram to show how reflection works and deduce the equation of Law of

Reflection.

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Images in Plane Mirror

When you look into the mirror, you see an image with 3 properties.

The image is______________ and ______________ (i.e Virtual images are images that are

formed in locations where light does not actually reach)

The image is the______________ size as you are

The image is located as far ______________ the mirror as you are in front of it.

Remember that the image is ______________ (left right reversal). If you raise a right hand, the

image will have a left hand raised. (eg. Ambulance) – this is called ______________ inversion.

The distance between you and the image is ______________ where d is the distance of the object

to the mirror.

______________ lines must be used for virtual images and virtual rays.

What portion of the mirror is required?

The diagram below depicts a 6-foot tall man standing in front of a plane mirror. To see the image of his

feet, he must sight along a line towards his feet; and to see the image of the top of his head, he must sight

along a line towards the top of his head. The ray diagram depicts these lines of sight and the complete

path of light from his extremities to the mirror and to the eye. In order to view his image, the man must

look as low as point Y (to see his feet) and as high as point X (to see the tip of his head). The man only

needs the portion of mirror extending between points X and Y in order to view his entire image. The

diagram depicts some important information about plane mirrors.

The man is twice as tall as the distance between points X and Y. In other words, to view an image of

yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. A 6-foot

tall man needs 3-feet of mirror (positioned properly) in order to view his entire image.

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Let’s try to solve with mathematical equation?

But what if the man stood a different distance from the mirror?

It can be shown that ______________ where the man stands, it will only take a mirror ______________

his height to obtain full view of himself.

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Multiple Reflections Angled Mirrors

Click to enlarge

180º - ______________ mirrors in a straight line reflect an object only once.

Click to enlarge

120º - Two mirrors set at any angle between 180º and 90º reflect an object 2 times. As the angle

approaches 90º, you see one mirror reflected in the other, but you do not see additional reflected objects.

Click to enlarge

90º - Two mirrors at a right angle (90º) show two complete reflections and one composite reflection. An

angle less than 90º shows two straight reflections and two partial reflections.

Click to enlarge

72º - At 72º you see______________ complete reflections.

Click to enlarge

60º - At 60º you see ______________ reflections – four straight and one composite.

Click to enlarge

45º - At 45º you see the object reflected 3 times in each mirror and one composite reflection for an

apparent total of ______________ reflections – or 8 if you count the object itself.

Unless the mirrors are very large, it is hard to see into an opening of less than 45º.

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Click to enlarge

Parallel - When two mirrors are parallel to each other, the number of reflections is ______________.

Placing one mirror at a slight angle causes the reflections to curve.

Click to enlarge

Multi-Faceted Mirrors - Increasing the number of flat mirrored surfaces or facets increases the number

of reflections, but what you see depends on where you stand. The number of complete and partial reflections changes as you view the mirror from different angles.

Reflectors on cars and Bicycle

Night reflectors glow when any light falls on them

Night or bicycle reflector

The ray of light incident on the

reflector are sent back in the same

direction

Total internal reflection takes place inside a reflector

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Periscope

Refraction

The ______________ of the light when light travels from one medium to another is called

refraction. Refraction happens because speed of light changes in different______________.

The extent to which the speed of light in a material medium differs from that in vacumn is

measured using the refraction______________.

Eg. Of refraction, straw appears bent in water.

Light travels faster in air than in glass, so light bends. Light bends towards the normal when the

speed decreases, light bends away from the normal when speed increases

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Snell’s Law

Snell’s Law of refraction states that when light travels from material with refractive index n1 into a

material with refractive index, n2. The angle of refraction 2 is related to the angle of incidence 1 by

If the incident ray is from air, then the equation can be further simplified to

If it is not from air but from other materials (i.e glass to water)

The ratio is a constant for whatever angle of incident.

The value of the ratio is called the______________ refractive index because it depends on the

properties of two different substances.

The bending of light always involves light travelling from one substance to another. It is not possible

to find the effect of a particular substance on the deflection of light without adopting one substance as

a reference standard. Once you have a standard, every substance can be compared with it. A natural

standard is a vacuum — the absence of any substance. The absolute refractive index of a vacuum is

given the value of 1. From this, the absolute refractive index of all other substances can be

determined.

Example 1

A ray of light strikes a piece of glass (n = 1.5), making an angle of 30o with the surface. What angle does

the refracted ray make with the surface inside the glass?

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Example 2

Using the information given in the following diagram, calculate the optical index of refraction for

medium B.

*additional notes: it is important to note that when a ray of light is directed from air to water, part of the

light is also reflected at the interface and the remainder is refracted. (refer to the diagram)

Refractive index and speed of light

Refractive index can also be expressed as a ratio of 2 speeds because light that is refracted slows down or

speeds up.

Example 3

Light travels at speeds of 2.34 x 108m/s in oil and at 2.00 x 10

8 m/s in glass and at 3.00 x 10

8m/s in a

vacuum. Calculate:

a) The absolute refractive index of oil

b) The absolute refractive index of glass and

c) The relative refractive index for light going from oil into glass.

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Thus, the relationship holds true:

Determine which medium is denser by using light refraction or snell’s law.

What is the final angle of refraction at point X? From the calculation, explain which medium is

denser.

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PASSING INTO LESS DENSE MEDIUM FROM DENSER MEDIUM

Critical Angle and Refractive Index

Critical angle only happens when light travels from optically ___________medium (higher index)

to a ___________medium (lower index). eg from glass to air or water to air.

Total Internal Reflection (TIR)

TIR happens when incident angle ___________ the critical angle and the rays are traveling from a

denser medium. No refraction is observed, all rays are reflected back into the medium.

Obtaining Expression for Critical Angle

Critical Angle: The largest incident angle which causes a refractive angle of 90º in a less dense medium.

The ray must travel from a denser to a less dense medium in order to make this happened.

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TIR (in practice)

The jug has a pea-sized hole drilled in its side such that when the cork is removed from the top of the jug,

water begins to stream out the jug's side. The beam of laser light is then directed into the jug from the

opposite side of the hole, through the water and into the falling stream. The laser light exits the jug

through the hole but is still in the water. As the stream of water begins to fall as a projectile along a

parabolic path to the ground, the laser light becomes trapped within the water due to total internal

reflection. Being in the more dense medium (water) and heading towards a boundary with a less dense

medium (air), and being at angles of incidence greater than the critical angle, the light never leaves the

stream of water. In fact, the stream of water acts as a light pipe to pipe the laser beam along its trajectory.

TIR and the Sparkle of Diamonds (in practice)

Relatively speaking, the critical angle for the diamond-air boundary is an extremely small number. Of all

the possible combinations of materials which could interface to form a boundary, the combination of

diamond and air provides one of the largest difference in the index of refraction values. This means that

there will be a very small nr/ni ratio and subsequently a small critical angle. This peculiarity about the

diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small

critical angle, light has the tendency to become "trapped" inside of a diamond once it enters. A light ray

will typically undergo TIR several times before finally refracting out of the diamond. Because the

diamond-air boundary has such a small critical angle (due to diamond's large index of refraction), most

rays approach the diamond at angles of incidence greater than the critical angle. This gives diamond a

tendency to sparkle. The effect can be enhanced by the cutting of a diamond gemstone with a

strategically planned shape. The diagram below depicts the total internal reflection within a diamond

gemstone with a strategic and a non-strategic cut. (refractive index for diamond= 2.417)

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The Optical Fibre

Optical fibres are also the basis of the important telecommunications industry. They allow high quality

transmission of many channels of information in a small cable over very long distances and with

negligible signal loss. The optical fibre is designed so that any ray meeting the outer surface of the glass

fibre is totally internally reflected back into the glass.

As shown in figure above, the light ray meets the edge of the fibre at an angle of incidence greater than

the critical angle and is reflected back into the fibre. In this way, nearly all of the light that enters the fibre

emerges at the other end.

If the glass fibre is exposed to the air, the critical angle for light travelling from glass to air is

______________, which is quite small. Any angle of incidence greater than this angle will produce total

internal reflection. If the fibre is very narrow, this angle is easily achieved. However, in both medical and

telecommunication uses, fibres are joined in bundles with edges touching. The touching would enable

light rays to pass from fibre to fibre, confusing the signal. To overcome this, a plastic coating is put

around the glass to separate the glass fibres. The total internal reflection occurs between the glass and the

plastic. The critical angle for light travelling from glass to plastic is ______________. This value presents

a problem because light meeting the edge of the glass at any angle less than ______________ will pass

______________ of the fibre.

Why do we see a red/orangey sky in the evening?

The colour of the sky is blue in midday and yellow during sunset because of a phenomena called

______________. The higher frequency colours like violet and blue are scattered ______________ by

the air particles and hence, we observe the sky is blue. However, during sunset, the light has to travel and

long distance and hence most of the higher frequency (low wavelength) colours have been scattered. The

lower frequency (long wavelength) light which is not readily scattered travels further to reach our eyes.

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Mirages (In Cold and Hot Countries)

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Dispersion of Light

Visible light, also known as white light, consists of a collection of component colors. These colors are

often observed as light passes through a triangular prism. Upon passage through the prism, the white light

is separated into its component colors - red, orange, yellow, green, blue and violet. The separation of

visible light into its different colors is known as dispersion.

Why does red light bend lesser than violet?

Light bends less if the speed is ______________ thus red light bends less.

Rainbow (Dispersion of Light)

Red is directed more steeply to the ground compared to blue and hence the observer often see red is often

at the top of the rainbow

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Lenses There are 2 types of lenses, convex and concave lens

BICONVEX LENS/CONVERGING LENS

Principal Axis : the line passing through the center of the lens which is _________to the lens

Principal focus : the point where all rays _______________

Focal length, f : the distance between ________________ and ______________ of lens

Converging lens focuses parallel light.

CONCAVE LENS/DIVERGING LENS

Diverging lens _________________ parallel light rays.

They diverge as if they come from a certain point behind the lens. This point is called the virtual

principal focus.

_________________ makes use of diverging lens.

Focal Length and Power

Power of a lens has a unit called _________________

The higher the power, the more light will bend, the shorter the focal length.

Thing lenses in contact, the power of combination = _________________

Diverging lenses has _________________ (vice versa)

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Image Formation by Converging Lens

Step 1: Draw principal axis and locate the focal length measure accurately (any deviation of focal

length on each side will cause image to be distorted)

Step 2: Draw ray 1, ray2 and ray3.

Step 3: Draw image.

CASE 1: If object is placed > 2f

You’ll get a smaller, inverted and real image. This arrangement is used in a camera.

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CASE 2: If the object is placed between f and 2f.

You’ll get a bigger, inverted, real image. This arrangement is used in projector

CASE 3: If the object is placed < f

You’ll get a larger, upright and virtual image. Thus arrangement is used in magnifying glass

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Image Formation by Diverging Lens

Step 1 : Draw principal axis, focal length

Step 2 : Draw ray 1, 2, and 3

Step 3 : Draw image

CASE 1 and Only ONE!!!

No matter where you place the object, diverging lens always forms a virtual image that is upright

and smaller than the object.

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The Thin Lens Equation and Magnification Equation

Thin Lens Equation

where u :

v :

f :

Distances to real objects and real images are _________________

Distances to virtual images are _________________

The focal length of a converging lens is _________________, because it has a real principal

focus, but that of a diverging lens is _________________

Magnification, m =

m(+ve) is for _________________ objects

m(-ve) is for _________________ objects

Example

Describe fully the image of a 4.0 cm object 15 cm in front of a convex lens with a focal length of 10 cm.

Answers:

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Example

Locate and describe the image formed by a 6.0 cm high object 15 cm in front of a concave lens with a

focal length of 10 cm.

Answer:

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Visible light

Wavelength