SNC2D · Unit 4 test review

Light & Geometric Optics: Test Review

Everything for the Unit 4 test on one page: the key facts from all 10 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

What Light Is: The Electromagnetic Spectrum and Sources of Light

Light is a transverse electromagnetic wave; it needs no medium and travels at $c = 3.00 \times 1 0^{8} m/s$ in a vacuum.
EM spectrum by increasing frequency (and energy): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
Visible light runs from about 700 nm (red) to about 400 nm (violet): ROY G BIV.
$c = f λ$ : a shorter wavelength means a higher frequency and more energy.
Light travels in straight lines in a uniform medium, so it can be drawn as rays.
Light sources are named by their energy input: incandescence, electric discharge, fluorescence, phosphorescence, chemiluminescence, bioluminescence, triboluminescence, LED.

Rays, the Laws of Reflection and Plane Mirrors

All angles are measured from the normal, the line perpendicular to the surface.
Law of reflection: $∠ i = ∠ r$ , and the incident ray, reflected ray and normal lie in one plane.
Specular reflection (smooth surface) forms images; diffuse reflection (rough surface) scatters light but still obeys the law at each point.
SALT describes an image: Size, Attitude, Location, Type.
Plane mirror image: same size, upright, same distance behind the mirror, virtual, and laterally inverted.
Real images form where light rays actually meet and can be projected; virtual images form where rays only appear to come from.

Concave and Convex Mirrors with Ray Diagrams

Concave mirrors converge parallel rays to F; convex mirrors diverge them as if from a virtual F behind the mirror.
Focal length is half the radius of curvature: $f = \frac{R}{2}$ .
Concave rays: parallel → through F; through F → parallel; through C → back on itself.
Concave mirror: object beyond C gives a smaller, inverted, real image between C and F; object inside F gives a larger, upright, virtual image behind the mirror; object at F gives no image.
Convex mirror: always smaller, upright, virtual, behind the mirror between V and F.

The Mirror and Magnification Equations

Mirror equation: $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$
Magnification: $M = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}$
$f$ is positive for concave mirrors and negative for convex mirrors.
$d_{i}$ positive means a real image in front of the mirror; $d_{i}$ negative means a virtual image behind it.
$M$ negative means inverted; $M$ positive means upright. Its size beyond or below 1 tells larger or smaller.

Refraction, Index of Refraction and the Speed of Light

Refraction is the change in direction of light at a boundary, caused by a change in speed.
Index of refraction: $n = \frac{c}{v}$ , with $c = 3.00 \times 1 0^{8} m/s$ ; $n$ has no units and is at least 1.
Into a larger $n$ (slower): bends toward the normal. Into a smaller $n$ (faster): bends away from the normal.
A ray along the normal changes speed but not direction.
Frequency stays the same across a boundary; speed and wavelength change.
Common indices: air 1.00, water 1.33, crown glass 1.52, diamond 2.42.

Snell's Law

Snell's law: $n_{1} sin θ_{1} = n_{2} sin θ_{2}$ , with both angles measured from the normal.
Solve for an angle with $sin θ_{2} = \frac{n _{1} sin θ _{1}}{n _{2}}$ , then take $sin^{- 1}$ .
From air: $n_{2} = \frac{sin θ _{1}}{sin θ _{2}}$ .
$\frac{n _{2}}{n _{1}} = \frac{sin θ _{1}}{sin θ _{2}} = \frac{v _{1}}{v _{2}}$
A ray through a block with parallel faces exits parallel to its original direction, displaced sideways.

Total Internal Reflection, the Critical Angle and Natural Phenomena

Total internal reflection needs light going from larger $n$ to smaller $n$ AND an angle of incidence greater than the critical angle.
Critical angle: $sin θ_{c} = \frac{n _{2}}{n _{1}}$ , where $n_{1} > n_{2}$ ; at $θ_{c}$ the refracted angle is $9 0^{\circ}$ .
Critical angles to air: water $48. 8^{\circ}$ , glass ( $1.50$ ) $41. 8^{\circ}$ , diamond $24. 4^{\circ}$ .
Fibre optics, binocular prisms and diamond sparkle all rely on total internal reflection.
Apparent depth (water, looking straight down) $\approx \frac{real depth}{1.33}$ ; mirages and shimmering come from air layers with different temperatures and indices.

Converging and Diverging Lenses with Ray Diagrams

Converging (convex) lenses are thicker in the middle; diverging (concave) lenses are thinner in the middle.
Converging rays: parallel → through F′; through O → straight; through F → parallel.
Diverging rays: parallel → as if from F (dashed); through O → straight; toward F′ → parallel.
Converging lens: object beyond 2F gives a smaller, inverted, real image (camera); between 2F and F gives a larger, inverted, real image (projector); inside F gives a larger, upright, virtual image (magnifier).
Diverging lens: always smaller, upright, virtual, on the object's side between F and the lens.
Real lens images form on the far side of the lens; virtual ones on the object's side.

The Thin Lens Equation and Magnification

Thin lens equation: $\frac{1}{f} = \frac{1}{d _{o}} + \frac{1}{d _{i}}$
Magnification: $M = \frac{h _{i}}{h _{o}} = - \frac{d _{i}}{d _{o}}$ ; negative $M$ means inverted.
$f$ is positive for converging lenses and negative for diverging lenses.
Positive $d_{i}$ : real image on the far side of the lens. Negative $d_{i}$ : virtual image on the object's side.
For a very distant object, the image forms at the focal point: $d_{i} \approx f$ .

The Eye, Vision Correction and Optical Devices

The eye forms a real, inverted, smaller image on the retina; the cornea does most of the focusing and the lens fine-tunes it.
Accommodation: the eye changes the shape of its lens to focus; a camera moves its lens instead.
Myopia (focus in front of the retina) is corrected with a diverging lens; hyperopia (focus behind) with a converging lens.
Lens power: $P = \frac{1}{f}$ in dioptres with $f$ in metres; negative power means a diverging lens.
Microscope total magnification = objective magnification × eyepiece magnification.
The largest telescopes are reflectors; binoculars use prisms and total internal reflection to make the image upright.

Where marks get lost

Thinking light needs air to travel. Light is an electromagnetic wave, not a vibration of particles, so it crosses the vacuum of space; sound is the wave that needs a medium. (What Light Is: The Electromagnetic Spectrum and Sources of Light)
Mixing up the direction of the spectrum. Radio waves have the longest wavelength and lowest frequency; gamma rays have the shortest wavelength and highest frequency and energy. (What Light Is: The Electromagnetic Spectrum and Sources of Light)
Forgetting to convert nanometres to metres before using $c = f λ$ . $650 nm$ is $6.50 \times 1 0^{- 7} m$ , not $650 m$ . (What Light Is: The Electromagnetic Spectrum and Sources of Light)
Confusing fluorescence and phosphorescence. Both absorb light and re-emit it; only phosphorescence keeps glowing after the source is removed. (What Light Is: The Electromagnetic Spectrum and Sources of Light)
Calling the Moon a light source. It is non-luminous: you see sunlight reflected from it. (What Light Is: The Electromagnetic Spectrum and Sources of Light)
Measuring the angle from the mirror surface instead of the normal. Always draw the normal first, then measure from it. (Rays, the Laws of Reflection and Plane Mirrors)
Saying the image is 'on the mirror' or 'in the glass'. A plane mirror image is behind the mirror, as far behind as the object is in front. (Rays, the Laws of Reflection and Plane Mirrors)
Calling a plane mirror image real because you can see it. You see virtual images too; a real image is one that can be projected onto a screen. (Rays, the Laws of Reflection and Plane Mirrors)
Thinking diffuse reflection breaks the law of reflection. Each point still obeys $∠ i = ∠ r$ ; the rough surface just tilts the normal from point to point. (Rays, the Laws of Reflection and Plane Mirrors)
Believing you need a mirror as tall as you are, or that stepping back lets you see more of yourself. Half your height is enough, at any distance. (Rays, the Laws of Reflection and Plane Mirrors)
Drawing the ray through F for a concave mirror reflecting through F again. A ray that arrives through F leaves parallel to the axis; a ray that arrives parallel leaves through F. (Concave and Convex Mirrors with Ray Diagrams)
Placing C at the focal point. C is twice as far from the mirror as F: $R = 2 f$ . (Concave and Convex Mirrors with Ray Diagrams)
Expecting a convex mirror to give an inverted or enlarged image for some object positions. Its image is always smaller, upright and virtual. (Concave and Convex Mirrors with Ray Diagrams)
Forgetting dashed lines for extensions behind a mirror. Light never travels behind a mirror, so anything drawn there must be dashed and the image there is virtual. (Concave and Convex Mirrors with Ray Diagrams)
Saying an object at F forms an image 'at infinity' and then describing its SALT. At F the reflected rays are parallel and no image forms. (Concave and Convex Mirrors with Ray Diagrams)
Forgetting to take the reciprocal at the end, and reporting $\frac{1}{d _{i}}$ as the image distance. (The Mirror and Magnification Equations)
Using a positive focal length for a convex mirror. Convex mirrors and diverging lenses have negative $f$ . (The Mirror and Magnification Equations)
Adding the reciprocals instead of subtracting: $\frac{1}{d _{i}} = \frac{1}{f} - \frac{1}{d _{o}}$ , not $\frac{1}{f} + \frac{1}{d _{o}}$ . (The Mirror and Magnification Equations)
Dropping the minus sign in $M = - \frac{d _{i}}{d _{o}}$ , which flips every upright/inverted conclusion. (The Mirror and Magnification Equations)
Calling $1/ (a + b)$ the same as $1/ a + 1/ b$ . You cannot flip each term separately; combine the fractions first, then flip. (The Mirror and Magnification Equations)
Saying light bends away from the normal when it slows down. Slower medium (larger $n$ ) means bending toward the normal. (Refraction, Index of Refraction and the Speed of Light)
Writing $n = \frac{v}{c}$ upside down. Since $v$ is never more than $c$ , an index below 1 is a sign the fraction was flipped. (Refraction, Index of Refraction and the Speed of Light)
Giving the index of refraction units. It is a ratio of two speeds, so the units cancel. (Refraction, Index of Refraction and the Speed of Light)
Assuming a ray along the normal bends. At $0^{\circ}$ incidence the speed changes but the direction does not. (Refraction, Index of Refraction and the Speed of Light)
Thinking frequency (colour) changes when light enters water. Speed and wavelength change; frequency stays the same. (Refraction, Index of Refraction and the Speed of Light)
Using radians mode, which makes every sine wrong. $sin 3 0^{\circ}$ must be exactly $0.5$ . (Snell's Law)
Cancelling the sines and treating the angles as proportional to $n$ . Take the sine first, do the arithmetic, then take the inverse sine. (Snell's Law)
Mixing up which medium is 1 and which is 2. Medium 1 is always the side the light is coming from. (Snell's Law)
Measuring the angles from the surface rather than the normal. (Snell's Law)
Not sanity-checking the direction: entering a larger index must give a smaller angle. (Snell's Law)
Thinking total internal reflection can happen when light goes from air into glass. It only happens going from a larger index to a smaller one. (Total Internal Reflection, the Critical Angle and Natural Phenomena)
Writing $sin θ_{c} = \frac{n _{1}}{n _{2}}$ with the larger index on top. That gives a value greater than 1 and an error on your calculator; the smaller index goes on top. (Total Internal Reflection, the Critical Angle and Natural Phenomena)
Saying the refracted ray at the critical angle is at $0^{\circ}$ . It is at $9 0^{\circ}$ to the normal, skimming along the surface. (Total Internal Reflection, the Critical Angle and Natural Phenomena)
Describing a mirage as an illusion inside the brain. The light really does curve; a camera photographs a mirage too. (Total Internal Reflection, the Critical Angle and Natural Phenomena)
Calling the reflection inside a raindrop 'total'. It is only a partial reflection (the light meets the back of the drop below the critical angle, so most of it passes out); refraction and dispersion are what separate the colours. (Total Internal Reflection, the Critical Angle and Natural Phenomena)
Mixing up lens and mirror names. A convex lens converges light, but a convex mirror diverges it. Go by what the light does: converging or diverging. (Converging and Diverging Lenses with Ray Diagrams)
Drawing the ray through the optical centre as bending. It passes straight through. (Converging and Diverging Lenses with Ray Diagrams)
Putting a lens's real image on the same side as the object. Light passes through a lens, so real images are on the far side. (Converging and Diverging Lenses with Ray Diagrams)
Using the far focal point F′ for the ray that should go through the near focal point F. The ray that leaves parallel is the one that passed through F on the object's side. (Converging and Diverging Lenses with Ray Diagrams)
Thinking that covering half a lens cuts off half the image. The whole image still forms, only dimmer. (Converging and Diverging Lenses with Ray Diagrams)
Using a positive focal length for a diverging lens. Diverging lenses have negative $f$ . (The Thin Lens Equation and Magnification)
Forgetting to flip at the end and reporting $\frac{1}{d _{i}}$ as $d_{i}$ . (The Thin Lens Equation and Magnification)
Mixing units, such as a focal length in mm with an object distance in m. (The Thin Lens Equation and Magnification)
Placing a lens's real image on the object's side. For a lens, positive $d_{i}$ is on the far side. (The Thin Lens Equation and Magnification)
Losing the minus sign in $M = - \frac{d _{i}}{d _{o}}$ and calling an inverted image upright. (The Thin Lens Equation and Magnification)
Correcting nearsightedness with a converging lens. Myopic eyes already converge light too strongly, so a diverging lens is needed. (The Eye, Vision Correction and Optical Devices)
Thinking the lens of the eye does most of the focusing. The cornea does about two-thirds of it; the lens fine-tunes. (The Eye, Vision Correction and Optical Devices)
Saying the eye focuses by moving its lens like a camera. The eye changes the lens's shape (accommodation). (The Eye, Vision Correction and Optical Devices)
Adding the objective and eyepiece magnifications. Total magnification is their product: $40 \times$ and $10 \times$ give $400 \times$ , not $50 \times$ . (The Eye, Vision Correction and Optical Devices)
Using centimetres in $P = \frac{1}{f}$ . Dioptres require the focal length in metres. (The Eye, Vision Correction and Optical Devices)

Practice test

20 questions from across the unit. Each one shows the lesson it comes from.

What Light Is: The Electromagnetic Spectrum and Sources of Light
1
Which list puts these waves in order of increasing frequency?
What Light Is: The Electromagnetic Spectrum and Sources of Light
2
Sort these visible colours from longest wavelength to shortest.
1. 1Blue
2. 2Green
3. 3Violet
4. 4Red
5. 5Orange
6. 6Yellow
Rays, the Laws of Reflection and Plane Mirrors
3
A ray strikes a plane mirror at $3 5^{\circ}$ to the mirror surface. What is the angle of reflection, in degrees?
°
Rays, the Laws of Reflection and Plane Mirrors
4
Put the steps for locating the image of a point in a plane mirror in order.
1. 1Mark the image where the dashed extensions cross
2. 2Extend the reflected rays backward behind the mirror as dashed lines
3. 3Draw each reflected ray so that the angle of reflection equals the angle of incidence
4. 4Draw two rays from the object point to the mirror
5. 5Draw the normal at each point of incidence
Concave and Convex Mirrors with Ray Diagrams
5
A concave mirror has a radius of curvature of $50 cm$ . What is its focal length, in cm?
cm
Concave and Convex Mirrors with Ray Diagrams
6
An object starts far from a concave mirror and moves steadily toward F. Sort the real image's size, from first to last.
1. 1Same size as the object
2. 2Very large and very far away
3. 3Larger than the object
4. 4Much smaller than the object
The Mirror and Magnification Equations
7
An object is $60.0 cm$ from a concave mirror with a focal length of $20.0 cm$ . Find the image distance, in cm, to 1 decimal place.
cm
The Mirror and Magnification Equations
8
A calculation gives a magnification of $M = - 2.0$ . Is the image upright or inverted? (One word.)
Refraction, Index of Refraction and the Speed of Light
9
Find the speed of light in diamond ( $n = 2.42$ ) in units of $1 0^{8} m/s$ , to 2 decimal places.
× 10⁸ m/s
Refraction, Index of Refraction and the Speed of Light
10
A laser beam strikes the flat surface of a block of glass exactly along the normal. What happens to the beam as it enters the glass?
Snell's Law
11
Light in air strikes glass ( $n = 1.50$ ) at $30. 0^{\circ}$ . Find the angle of refraction, to the nearest tenth of a degree.
°
Snell's Law
12
Sort the steps for finding a refracted angle with Snell's law.
1. 1Check that the ray bent the correct way
2. 2Take the inverse sine to get $θ_{2}$
3. 3Substitute and calculate the value of $sin θ_{2}$
4. 4Identify medium 1 (where the light comes from) and medium 2
5. 5Rearrange to $sin θ_{2} = \frac{n _{1} sin θ _{1}}{n _{2}}$
Total Internal Reflection, the Critical Angle and Natural Phenomena
13
Find the critical angle for light travelling from water ( $n = 1.33$ ) into air, to the nearest tenth of a degree.
°
Total Internal Reflection, the Critical Angle and Natural Phenomena
14
Why do binoculars use glass prisms instead of silvered mirrors to fold the light path?
Converging and Diverging Lenses with Ray Diagrams
15
Which lens is thicker in the middle than at its edges?
Converging and Diverging Lenses with Ray Diagrams
16
Sort the steps for drawing a converging-lens ray diagram.
1. 1Describe the image using SALT
2. 2Mark the image tip where the refracted rays (or their dashed extensions) cross
3. 3From the object's tip, draw two principal rays: one parallel to the axis that refracts through F′, and one straight through the optical centre
4. 4Draw the principal axis, the lens line and mark F, 2F, F′ and 2F′
5. 5Draw the object as an upright arrow at the given position
The Thin Lens Equation and Magnification
17
An object is $45.0 cm$ from a converging lens with $f = 15.0 cm$ . Find the image distance in cm, to 1 decimal place.
cm
The Thin Lens Equation and Magnification
18
A very distant object is viewed through a converging lens with $f = 35 mm$ . About how far behind the lens does the image form, in mm? (Type the number.)
The Eye, Vision Correction and Optical Devices
19
A student can read the board up close but sees distant signs as blurry. Which condition and correction match?
The Eye, Vision Correction and Optical Devices
20
What is the name of the eye's process of changing the shape of its lens to focus on objects at different distances?

Endless drill

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Light & Geometric Optics: Test Review

Key facts

Where marks get lost

Practice test

Endless drill

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