Sound, light and vision

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Explain sound as vibration
Distinguish amplitude from frequency and their effects

Vocabulary: vibration · amplitude · frequency · pitch · loudness · hertz

Retrieve previous learning

What is a repeated movement around a rest position?

Check: A vibration or oscillation.

Learn the concept

A sound begins when an object vibrates and makes neighbouring material move. A drum skin moves back and forth after a strike; the movement may become too small to see while the sound continues. A voice begins with vibrating vocal folds. A sound source can be hidden, so identify what is moving rather than assuming every visible object is the source.

Amplitude describes the size of the vibration measured from its resting position. A larger amplitude usually transfers more energy and can produce a louder sound. Frequency is the number of complete vibrations each second, measured in hertz (Hz). Higher frequency is heard as higher pitch. Striking the same drum harder mainly changes amplitude; tightening its skin can change frequency. Do not use 'high' ambiguously: say high pitch or high loudness.

A diagram of a vibrating ruler needs a marked rest line and extreme positions. The distance from rest to one extreme is amplitude; the distance from one extreme to the other is twice that amplitude. Counting 400 complete cycles in two seconds gives 200 Hz, not 400 Hz. Sound intensity at a listener also depends on distance and surroundings, so source amplitude alone does not fix what every listener hears.

Worked model

A string completes 800 back-and-forth cycles in 4 s.
Frequency = cycles ÷ time = 800 ÷ 4 = 200 Hz.
If it is displaced 3 mm from rest at either extreme, amplitude is 3 mm; peak-to-peak travel is 6 mm.

Guided practice

A string makes 600 cycles in 3 s. What is its frequency, and what change would generally raise its pitch?

Hint: Divide complete cycles by seconds; relate pitch to frequency.

Check the guided answer

600 ÷ 3 = 200 Hz. A change that makes the string vibrate more often each second raises pitch.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“Louder sounds always have higher pitch.”

Correction: Loudness and pitch describe different properties: amplitude and frequency respectively.

Extend and reflect

How could a recording help compare two notes?

Guidance: Compare repetition rate over equal time windows and wave height on the same scale; do not infer exact perceived loudness from an uncalibrated display.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Explain sound as vibration. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Travelling vibrations

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Describe transfer of vibration through a material
Distinguish particle oscillation from movement of the wave

Vocabulary: medium · particle · compression · rarefaction · energy transfer

Retrieve previous learning

What begins a sound at the source?

Check: An object vibrates and disturbs neighbouring material.

Learn the concept

A vibrating loudspeaker cone pushes on nearby air and then moves back. Neighbouring air is alternately compressed and spread out. Those changes pass from one region to the next; the same pocket of air does not travel from the speaker all the way to an ear. The disturbance and its energy travel while air particles oscillate around their usual positions.

The material carrying a sound is called its medium. Air, water and a solid surface can carry vibrations. A pupil can model this with a line of loosely coupled objects: move the first object back and forth, then follow the disturbance through the line while checking that each object stays near its own place. The model is limited because air molecules move in three dimensions and collide, rather than being attached like springs.

Where a sound travels through air, the oscillation of air is broadly parallel to the direction of the travelling disturbance. A drawing of crowded and uncrowded regions shows compressions and rarefactions; it must not be read as a photograph of permanently crowded particles. Do not use a transverse rope drawing as proof of the direction of air motion.

Worked model

Mark three nearby air regions A, B and C beside a speaker.
The forward cone movement compresses A; A's disturbance influences B and then C.
Each region oscillates locally, while the pattern reaches C later than A.

Guided practice

Does the air beside a speaker travel to the back of the room as the sound travels?

Hint: Track one region and the disturbance separately.

Check the guided answer

No. Air particles oscillate locally; the changing compression pattern and energy pass onward through successive regions.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“The particles travel along with the sound from source to listener.”

Correction: The sound disturbance travels; particles of the medium oscillate mainly near their positions.

Extend and reflect

Compare the sound and a queue of people passing a message.

Guidance: Explain what is passed along and why people need not move down the queue; state that a message analogy does not model compressions.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Describe transfer of vibration through a material. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Travelling sound

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Explain why sound needs a medium
Compare sound speed and received sound at different distances

Vocabulary: vacuum · medium · speed · distance · energy spreading

Retrieve previous learning

What moves through the air when sound travels?

Check: A vibration pattern and energy pass from one region to another; air particles oscillate locally.

Learn the concept

Sound needs particles or another mechanical medium to pass a disturbance. In a vacuum there are no particles to carry ordinary sound. Light can cross a vacuum, which makes sound and light different despite both being described with wave language. A silent space scene with a distant explosion is cinematic convention, not an accurate account of sound travelling through empty space.

Sound speed depends on the medium and its conditions. At ordinary room conditions it is about 340 m/s in air. It is generally faster in water and many solids than in air because their mechanical properties permit quicker transfer, but 'solids are always fastest' is too broad without specifying the material and temperature. A one-way 680 m journey through air takes about 680 ÷ 340 = 2 s; an echo makes a round trip.

As sound spreads from a small source, its energy is distributed over a larger region, so it is usually quieter farther away. Absorption, barriers and reflections can alter this. A classroom comparison must keep source output and measuring position controlled; 'quieter' does not mean the sound has slowed down. Protect hearing and avoid generating high sound levels for demonstration.

Worked model

An echo returns 0.8 s after a shout in still air at approximately 340 m/s.
The disturbance travels out and back, so total path = 340 × 0.8 = 272 m.
Distance to the wall is half the path, 136 m. State that this is an approximation for the assumed air conditions.

Guided practice

Why can an astronaut see a distant event through a spacecraft window yet not hear it through empty space?

Hint: Compare the media needed by light and sound.

Check the guided answer

Light can travel through the vacuum; sound requires a mechanical medium and cannot cross the vacuum between the event and spacecraft.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“A quieter sound must be moving more slowly.”

Correction: Received loudness and wave speed are distinct; distance can reduce intensity while speed in the same medium remains approximately unchanged.

Extend and reflect

An echo is heard after 0.5 s. Estimate wall distance at 340 m/s.

Guidance: Use the round trip: 340 × 0.5 ÷ 2 = 85 m; justify dividing by two.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Explain why sound needs a medium. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Reflecting and absorbing sound

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Distinguish reflection from absorption of sound
Evaluate a noise-reduction design with evidence

Vocabulary: reflection · absorption · echo · reverberation · fair comparison

Retrieve previous learning

Why can an echo require more travel time than a one-way sound?

Check: The sound travels to a reflecting surface and back to the listener.

Learn the concept

A reflected sound changes direction at a surface and can reach a listener later than the direct sound. A distinct echo requires sufficient delay; many reflections arriving close together produce reverberation. A material can reflect some sound, absorb some by converting some wave energy into other forms such as heat, and transmit some. Avoid calling any ordinary wall a perfect reflector or absorber.

Surface shape, thickness, frequency and installation all matter. A soft, porous panel may reduce reflections inside a room, but it is not automatically an effective barrier against outside noise. Heavy sealed construction and gaps around a door affect transmission. A design claim should specify whether the aim is to reduce reflected sound in the room or sound entering another room.

To compare two panels, use the same source, microphone, distance, room layout and frequency range. Measure or describe the result before judging. A smartphone reading alone may be uncalibrated; repeated readings and a stated limitation make the conclusion more honest. Keep the sound level safe for hearing.

Worked model

Problem: speech in a hall is hard to understand because reflections linger.
Choose a treatment aimed at absorption inside the hall, such as suitable wall or ceiling panels, while considering fire and installation standards.
Compare speech clarity or measured decay under the same conditions before and after; do not promise complete silence.

Guided practice

Would a thin soft wall hanging necessarily stop traffic noise entering through a leaky window?

Hint: Separate indoor reflection from transmission through gaps.

Check the guided answer

No. It may reduce reflections inside, but outside noise can pass through the window and gaps; sealing and suitable barrier design address a different problem.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“Soft materials always soundproof a room.”

Correction: Absorbing reflections within a room and blocking transmission through its boundaries are different design tasks.

Extend and reflect

Why might a panel help speech clarity but not bass from another room?

Guidance: Discuss frequency-dependent absorption and transmission without claiming a precise performance figure for an unspecified material.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Distinguish reflection from absorption of sound. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Shadows

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Explain a shadow using light rays and an opaque object
Predict a shadow change when source position changes

Vocabulary: ray · opaque · transparent · translucent · umbra · penumbra

Retrieve previous learning

Can light travel through a vacuum?

Check: Yes. Unlike sound, light does not need a material medium.

Learn the concept

In a uniform material, light is modelled as travelling in straight lines. A ray diagram uses arrows to show its direction; a ray is a model, not a thin solid object. An opaque object blocks light travelling to a screen, leaving a darker region behind it. A transparent material lets much light through; a translucent material scatters transmitted light, so its shadow may be less sharp.

A small source can form a relatively sharp shadow. An extended source produces a darker full-shadow region (umbra) and a partial-shadow region (penumbra), because different parts of the source may remain visible from different points on the screen. The position and size of a shadow depend on source, object and screen geometry. Moving an object nearer a small source generally makes its screen shadow larger when the screen stays fixed.

To predict rather than guess, draw two boundary rays from the edges of the source past opposite edges of the object to the screen. Mark the area the rays cannot reach. A classroom light source should be low voltage and teacher approved; never look into a bright lamp or the Sun to trace rays.

Worked model

Place a 4 cm object midway between a small source and a screen, with 20 cm source-to-object and 40 cm source-to-screen distances.
Similar triangles give shadow height ÷ 4 cm = 40 ÷ 20 = 2.
The ideal small-source shadow is 8 cm high; a broad source would add a penumbra and blur the boundary.

Guided practice

What happens to a screen shadow when an opaque object moves closer to a small source while screen position stays fixed?

Hint: Draw boundary rays diverging from the source.

Check the guided answer

Its shadow generally grows larger because the object's angular size seen from the source increases.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“A shadow is a substance emitted by an object.”

Correction: A shadow is a region receiving less light because the object blocks some paths from the source.

Extend and reflect

How would the diagram change if the screen moved farther from a small source?

Guidance: Keep source and object fixed, trace the same boundary rays farther, and predict a larger ideal shadow.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Explain a shadow using light rays and an opaque object. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Reflecting light from mirrors

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Use a normal to measure incidence and reflection angles
Plan a safe ray-tracing comparison

Vocabulary: incident ray · reflected ray · normal · angle of incidence · angle of reflection

Retrieve previous learning

How does a ray diagram represent light travel in a uniform medium?

Check: Straight lines with arrows indicate direction.

Learn the concept

When a narrow light beam reaches a plane mirror, the reflected ray leaves on the same side of the surface as the incoming ray. Draw a normal at the contact point: a line at 90° to the mirror. The angle of incidence is between incoming ray and normal, and the angle of reflection is between outgoing ray and normal. Measuring from the mirror surface instead gives complementary angles and can hide a method error.

For a plane mirror the reflection angle equals the incidence angle, within measurement uncertainty. A 35° incident angle measured from the normal produces a reflected angle of about 35° from that normal. Measure each angle between its ray and the normal at the mirror. The rule does not mean that the outgoing ray always points back along the incoming path; that occurs only at normal incidence.

A practical comparison needs a low-voltage ray box, a stable mirror, paper and a protractor. Mark incident and reflected paths before moving the mirror, draw the normal at each contact point, and repeat for several starting angles. A teacher checks electrical and eye safety; do not point beams at faces or use a laser without an approved risk assessment.

Worked model

Draw a horizontal mirror and a vertical normal at the point where a ray arrives.
Measure 25° between incoming ray and normal.
Draw the outgoing ray on the other side of the normal at about 25°; label both angles from the normal.

Guided practice

A learner measures 60° between a ray and the mirror surface. What is its incidence angle?

Hint: The normal and mirror surface are perpendicular.

Check the guided answer

90° − 60° = 30° from the normal.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Teacher observed practical evidence

A teacher must apply the school's risk assessment, allergy policy and any individual healthcare plan before the practical. Observe and record the criteria during supervised work. Written answers cannot certify practical safety or skill.

Teacher verifies safe beam handling and stable mirror
Teacher observes measured angles from the normal and records repeat uncertainty

Find and correct a misconception

“Reflection angles are measured between the beam and the mirror surface.”

Correction: The conventional incidence and reflection angles are measured from the normal to the surface.

Extend and reflect

Why might a measured pair be 39° and 41° rather than equal?

Guidance: Discuss thick pencil lines, mirror placement, protractor resolution and repeat measurements before claiming the law failed.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Use a normal to measure incidence and reflection angles. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

How we see things

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Trace light from a source or reflecting object into an eye
Explain why an eye cannot see in complete darkness

Vocabulary: light source · reflection · retina · pupil · ray diagram

Retrieve previous learning

Which direction does a reflected ray move after striking a mirror?

Check: Away from the mirror, with reflection angle equal to incidence angle from the normal.

Learn the concept

Seeing requires light to enter the eye. A lamp is a source that emits light; a book is usually seen because light from a source falls on it and some is reflected into the eye. Draw arrows from the lamp to the book and from the book to the eye. The arrow must not start at the eye and travel outward to 'find' the book.

The pupil is an opening that admits light. The lens helps focus it onto the light-sensitive retina, where signals begin that the brain interprets. This is a simplified account: identifying an object also uses processing, prior experience and contrast. A mirror can redirect light into the eye but does not make light when it reflects it.

In complete darkness there is no light from the object to enter the eye, even if the eye is open and looking directly at it. In dim light a pupil can widen but cannot create light. A model should distinguish a luminous object from a non-luminous object and identify a plausible source for the latter. Never look directly at the Sun or a very bright beam to test vision.

Worked model

A person reads a page under a desk lamp.
Trace lamp → page to show illumination, then page → eye to show reflected light entering the pupil.
The page is not itself a light source; the eye does not project a seeing beam.

Guided practice

Why can you see a white cup in a lit room but not in complete darkness?

Hint: Name the source and path into the eye.

Check the guided answer

Room light reaches the cup and some is reflected into the eye. In complete darkness that reflected path has no light to carry.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“Eyes send out light to illuminate whatever we look at.”

Correction: Light from a source or lit object enters the eye; eyes do not emit the light used for ordinary vision.

Extend and reflect

What changes in your diagram when you look at a lit phone screen?

Guidance: Show light emitted by the screen entering the eye; room light may also reflect from the glass.

Where this lesson could lead · Combined Science: Trilogy GCSE → Daskerel Physical Sciences

This lesson practises: Trace light from a source or reflecting object into an eye. Scientific explanation, measurement and evidence support later laboratory, technical and quality work.

Next school subject: Combined Science: Trilogy GCSE. Check the subject and examination board that fit your school.
Later DASKEREL learning: Daskerel Physical Sciences. Explore further study and build evidence from practical work.
Later credential exploration: No subject-specific professional credential is mapped from this lesson. Explore the credential catalogue after choosing a later specialism.
Example career direction: Laboratory Data Analyst. Explore organisations and local support.

This is an exploratory route, not a promise of admission, a qualification, certification eligibility or employment. Years 7–9 learning is an early foundation; any later credential may require substantial study, experience or local approval.

Year 7 · Physics: waves · original lesson pack

DASKEREL beta · internal AI review pending

Reflections in mirrors

DASKEREL wrote this teaching and practice using Oak's sequence as a source. View the source lesson at Oak National Academy. Oak has not endorsed this material. Check Oak's terms and separate rights for third-party works.

Learning outcomes

Locate a virtual image behind a plane mirror with a ray diagram
Describe its size, orientation and apparent depth

Vocabulary: virtual image · plane mirror · apparent depth · lateral inversion · line of sight

Retrieve previous learning

From which line are incidence and reflection angles measured?

Check: From the normal at the point where the ray meets the mirror.

Learn the concept

A plane mirror redirects rays from an object to an eye. The brain interprets the outgoing rays as if they had travelled in straight lines from behind the mirror. Extend two reflected rays backwards as dashed lines: their apparent meeting point locates a virtual image. No light actually gathers at that point, so a screen placed behind the mirror cannot catch that image.

For a flat mirror, the virtual image appears the same perpendicular distance behind the mirror as the object is in front. It is upright and the same size in the simple plane-mirror model. A person 1.2 m in front sees an apparent image 1.2 m behind, making the person-to-image separation 2.4 m. Changing the viewer's position changes which rays reach the eye but not the modelled location of a fixed object's image.

A mirror seems to swap left and right, but it more precisely reverses front and back relative to its surface. A printed word appears reversed because its front-facing orientation is compared with the mirror view. To make a robust explanation, mark a feature on the object's right and trace how its apparent position is seen; do not claim that the mirror physically moves parts of the object.

Worked model

Place a small object 20 cm in front of a vertical plane mirror.
Draw two rays from the object to different points on the mirror, reflect each using equal angles, and extend outgoing rays behind the mirror as dashed lines.
The extensions meet 20 cm behind the mirror; the image is virtual, upright and same size in the ideal model.

Guided practice

A candle is 35 cm in front of a plane mirror. How far behind the mirror does its image appear?

Hint: Compare perpendicular distances from the mirror.

Check the guided answer

35 cm behind the mirror, giving 70 cm from candle to its apparent image.

Independent practice

Write your own response to every question before viewing the model answers. Your writing stays in this page session; this activity does not submit, store or grade it. Avoid including private information.

Find and correct a misconception

“A mirror image is a real object behind the glass.”

Correction: The image is virtual: reflected rays only appear to originate behind a plane mirror.

Extend and reflect

Why does a mirror image remain the same size as you step back while it occupies less of your field of view?

Guidance: Separate physical image size in the plane-mirror model from apparent angular size at the eye as distance increases.