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Reflection and Refraction

Reflection and Refraction — American System Physics Revision Notes & Topical Questions

5 min read 6 parts Lesson 1 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Reflection and Refraction: Mirrors, Refraction and Lenses — AMERICAN SYSTEM PHYSICS notes: Apply the law of reflection, Snell's law and the mirror and lens equation to locate and describe images and explain total internal reflection.The law of reflection has two parts: angle of i…

  • lateral inversion
  • critical angle
  • Magnification
  • short sight (myopia)
  • Worked example 1
  • Worked example 2

Section 1 of 6Reflection and plane mirrors

The law of reflection has two parts: angle of incidence i equals angle of reflection r (both measured from the normal), and the incident ray, reflected ray and normal lie in one plane.

Reflection and plane mirrors
A ray along the normal (i = 0°) reflects straight back.
In specular reflection a smooth surface reflects rays in one direction.
In diffuse reflection each part of a rough surface faces a different way and has its own normal; every ray still obeys i = r but the reflected rays spread out,
  • which is why we can see non-luminous objects from any direction.
    • (a sheet of paper in a lit room)

To find the image in a plane mirror, draw two rays from a point on the object, reflect each with i = r, then extend the reflected rays backward as dashed lines; the image is where they cross.

The image is the same distance behind the mirror as the object is in front, and the line joining object and image is perpendicular to the mirror.
Virtual
A plane mirror image is virtual (rays only appear to come from it; a screen there shows nothing), upright, same size and laterally inverted (lateral inversion: left-right reversal,
  • which is why AMBULANCE is printed reversed).
Uses include periscopes (two mirrors at 45°), dressing mirrors and making a room look larger.
Reflection happens for all waves (sound echoes, water waves at a barrier) and the reflected wave keeps the same speed, frequency and wavelength.
Rotating a mirror by an angle turns the reflected ray through twice that angle.

Section 2 of 6Refraction and total internal reflection

Refraction is the change in direction of a wave as it enters another medium, caused by a change in speed; frequency stays constant while speed and wavelength change.

Into a denser medium light bends towards the normal, out of it away from the normal.
What the symbols mean:
Snell's law: n1sin θ1 = n2sin θ2, with refractive index n = sin i/sin r = c/v.
What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction (both measured from the normal)
Mediumn
Vacuum/air1.00
Water1.33
Glass1.52
Diamond2.42

The critical angle c is the angle of incidence in the denser medium for which the angle of refraction is exactly 90°; sin c = 1/n for a boundary with air.

Refraction and total internal reflection
Total internal reflection needs light going from dense to less dense with i greater than c; optical fibres use it.
Different colours have slightly different n, causing dispersion in a prism.

Section 3 of 6Mirrors, lenses and image formation

The mirror/lens equation is 1/f = 1/do + 1/di.

US sign convention: real image distance positive, virtual negative; a diverging lens and convex mirror have negative f.
Magnification
For a concave mirror f = R/2. Lens power P = 1/f (f in metres), in dioptres (D). Magnification m = hi/ho = di/do, no unit.
Describe an image with three words: real or virtual, upright or inverted, enlarged, diminished or same size.
DeviceTypeImages
Plane mirror-virtual, upright, same size
Concave mirrorconvergingreal inverted (object beyond f) or virtual upright (inside f)
Convex mirrordivergingvirtual, upright, smaller (wide field, used as car wing mirror)
Convex lensconvergingreal inverted or virtual magnified
Concave (diverging) lensdivergingvirtual, upright, smaller

A diverging lens is thinner in the middle and spreads parallel rays as if from the principal focus.

A magnifying glass needs the object inside F.
An object at 2F of a converging lens gives a real, inverted, same-size image at 2F.
The eye's cornea and lens form a real, inverted, diminished image on the retina.
Short sight (myopia)
In short sight (myopia) the eyeball is too long (or lens too strong), focusing in front of the retina, so a diverging lens spreads the rays first.
In long sight the eyeball is too short, so a converging lens adds convergence.

Section 4 of 6Worked examples

  1. A ray hits a plane mirror with angle of incidence 40°. What is the angle between the reflected ray and the mirror surface? [2]2 marks

  2. An object is 30 cm in front of a plane mirror. How far is the image from the object? [1]1 mark

  3. A convex lens has f = 10 cm and the object is 30 cm away. Find the image and describe it. [3]3 marks

  4. f = 20 cm and do = 60 cm. Find di. [2]2 marks

  5. An object 4.0 cm tall gives an image 1.0 cm tall. Find the magnification. [1]1 mark

  6. Explain why a mirror rotated by 15° turns the reflected ray (fixed incident ray) through 30°. [2]2 marks

Section 5 of 6Key terms

TermMeaning
Reflected rayThe ray leaving a surface after reflection.
Lateral inversionThe left-right reversal of an image in a plane mirror.
RefractionChange in direction of a wave on entering another medium, caused by a change in speed.
Critical angleAngle of incidence in the denser medium giving 90° refraction; sin c = 1/n.
Diverging (concave) lensA lens thinner in the middle that spreads parallel rays.
MagnificationImage height divided by object height, m = hi/ho.
Short sight (myopia)Defect where light is focused in front of the retina; corrected by a diverging lens.

Section 6 of 6Exam technique

1
Measuring the angle of incidence from the mirror surface — measure it from the normal.
2
Calling a plane mirror image inverted — it is upright but laterally inverted.
3
Saying rough surfaces do not obey the law of reflection — each ray does, but normals vary.
4
Calling an image real because you can see it — virtual images cannot be formed on a screen.
5
Applying total internal reflection from less dense to denser medium — it needs dense to less dense.

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