Unit 13 - Grade 11-12 Physics

Light and Optics

Study light as an electromagnetic wave, reflection, refraction, Snell's law, total internal reflection, dispersion, color, mirrors, lenses, ray diagrams, image formation, and optical instruments.

Lesson roadmap

What Students Should Master in This Unit

Optics explains how light travels, bends, reflects, forms images, separates into colors, and powers everyday technologies such as cameras, glasses, microscopes, telescopes, fiber optics, and projectors.

Model light rays and waves

Use ray diagrams, wave properties, electromagnetic spectrum ideas, and image vocabulary.

Analyze reflection and refraction

Apply law of reflection, index of refraction, Snell's law, critical angle, and dispersion.

Solve mirror and lens problems

Use focal length, mirror/lens equations, magnification, sign conventions, and ray tracing.

Quick navigation

Jump to a Topic

Light Basics Optics Images EM Spectrum Reflection Refraction Snell's Law Total Internal Reflection Dispersion and Color Mirrors Lenses Optical Instruments Simulation Labs Lab Skills Worked Examples Practice Problems
Light as a wave and ray

1. Light Basics

Light is electromagnetic radiation. In many optics problems, light can be modeled as rays that travel in straight lines through uniform media. In wave optics, light is modeled using wavelength, frequency, interference, and diffraction.

Light as rays and waves Light can be modeled as rays or electromagnetic waves ray model: straight paths wave model: c = fλ
Use the ray model for reflection, refraction, mirrors, and lenses; use the wave model for wavelength, frequency, color, and interference ideas.
Speed of light in vacuum c = 3.00 × 108 m/s Fastest speed for light in vacuum.
Wave equation c = fλ For electromagnetic waves in vacuum.
Speed in a medium v = c/n n is the index of refraction.

Ray Model Vocabulary

  • Incident ray: incoming light ray.
  • Reflected ray: ray that bounces from a surface.
  • Refracted ray: ray that enters a new medium and changes direction.
  • Normal: imaginary line perpendicular to a surface at the point of contact.
  • Optical axis: central reference line through a mirror or lens.
Visible light inside a larger family

3. Electromagnetic Spectrum

Visible light is only a small part of the electromagnetic spectrum. All electromagnetic waves travel at speed c in vacuum, but they differ in wavelength, frequency, and photon energy.

Electromagnetic spectrum Visible light is one narrow part of the EM spectrum radio microwave IR visible UV X-ray gamma long wavelength, low frequency short wavelength, high frequency
As wavelength decreases across the spectrum, frequency and photon energy increase.
Region Relative Wavelength Common Uses or Examples
Radio wavesLongestCommunication, broadcasting, astronomy.
MicrowavesLongCooking, radar, Wi-Fi.
InfraredLonger than red lightThermal imaging, remote controls.
Visible lightAbout 400 nm to 700 nmHuman vision.
UltravioletShorter than violet lightFluorescence, sterilization, sunburn.
X-raysVery shortMedical imaging.
Gamma raysShortestNuclear processes, cancer treatment.
Photon energy E = hf Higher frequency means higher photon energy.
Photon energy with wavelength E = hc/λ Shorter wavelength means higher energy.
Visible range estimate 400 nm < λ < 700 nm Violet is shorter wavelength; red is longer wavelength.
Light bouncing from surfaces

4. Reflection

Reflection occurs when light bounces from a surface. For a smooth surface, the reflected rays form a clear image. For a rough surface, reflected rays scatter.

Law of reflection Angles are measured from the normal θi θr normal θi = θr
The incident angle equals the reflected angle, and both angles are measured from the normal line.
Law of reflection θi = θr Angles are measured from the normal.
Plane mirror distance dimage = dobject Image appears same distance behind mirror as object is in front.
Plane mirror magnification m = +1 Image is upright and same size.

Plane Mirror Image Properties

  • Virtual, upright, same size, laterally inverted.
  • Image distance equals object distance.
  • The image appears behind the mirror, but light rays do not actually meet there.
Light changing speed and direction

5. Refraction

Refraction happens when light enters a new medium and changes speed. If the light hits at an angle, its direction changes too.

Refraction at a boundary Light bends when speed changes at a boundary lower n, faster v higher n, slower v bends toward normal
When light enters a higher-index medium at an angle, it slows down and bends toward the normal.
Index of refraction n = c/v Higher n means light travels slower in that medium.
Speed in medium v = c/n c is speed of light in vacuum.
Frequency stays same f1 = f2 When light enters a new medium, frequency stays constant.

Direction Rules

  • Entering a higher-index medium: light slows and bends toward the normal.
  • Entering a lower-index medium: light speeds up and bends away from the normal.
  • At normal incidence, light changes speed but does not bend direction.
Calculating refraction angles

6. Snell's Law

Snell's law connects the angle of incidence, angle of refraction, and refractive indices of the two media.

Snell's law calculation setup Use refractive index and angle to predict bending n1 n2 n1 sin(θ1) = n2 sin(θ2) measure both angles from the normal
Snell's law is reliable only when the angles are measured from the normal, not from the surface.
Snell's law n1 sin(θ1) = n2 sin(θ2) Angles are measured from the normal.
Wavelength relation λmedium = λvacuum/n Frequency stays the same, so wavelength changes.
Relative speed relation v1/v2 = n2/n1 Higher index means lower speed.
Common mistake: Angles in Snell's law are measured from the normal, not from the surface.
When refraction stops and all light reflects

7. Total Internal Reflection

Total internal reflection occurs when light tries to travel from a higher-index medium to a lower-index medium at an angle greater than the critical angle.

Total internal reflection Beyond the critical angle, all light reflects internally critical ray reflected ray n1 > n2 sin(θc) = n2/n1
Total internal reflection occurs only when light starts in the higher-index medium and the incident angle exceeds the critical angle.
Critical angle sin(θc) = n2/n1 Only when n1 > n2.
Critical condition θ2 = 90° The refracted ray would travel along the boundary.
Total internal reflection θ1 > θc All light reflects inside the high-index medium.

Applications

  • Fiber optic cables.
  • Medical endoscopes.
  • Prisms in binoculars.
  • Diamond sparkle due to high refractive index and internal reflections.
Separating and mixing colors

8. Dispersion and Color

Dispersion occurs when index of refraction depends on wavelength. In glass, violet light usually bends more than red light, so white light spreads into a spectrum.

Dispersion and color Different wavelengths refract by different amounts white light red bends less violet bends more
Dispersion separates white light because each color has a different wavelength and a slightly different refractive index in glass.
Red light longer λ, lower f Bends less in normal glass dispersion.
Violet light shorter λ, higher f Bends more in normal glass dispersion.
White light mixture of visible colors A prism separates the mixture by wavelength.

Color Mixing

  • Additive color: light colors add. Red + green + blue can make white light.
  • Subtractive color: pigments or filters remove wavelengths from white light.
  • An object appears a color because it reflects/transmits that color and absorbs others.
Image formation by reflection

9. Mirrors

Curved mirrors form images by reflection. Concave mirrors can form real or virtual images depending on object position. Convex mirrors always form virtual, upright, reduced images.

Curved mirror ray diagram Concave mirrors can focus parallel rays C F object 1/f = 1/do + 1/di
Concave mirrors use reflected principal rays to locate real or virtual images depending on object distance.
Mirror equation 1/f = 1/do + 1/di do object distance, di image distance.
Magnification m = hi/ho = -di/do Negative m means inverted image.
Focal length and radius f = R/2 For spherical mirrors.

Mirror Types

  • Concave mirror: converging mirror; can create real inverted images or virtual upright magnified images.
  • Convex mirror: diverging mirror; creates virtual upright reduced images with wide field of view.
  • Plane mirror: creates virtual upright same-size images.
Image formation by refraction

10. Lenses

Lenses form images by refracting light. Converging lenses are thicker in the center, while diverging lenses are thinner in the center.

Converging and diverging lenses Lens shape determines whether rays converge or diverge converging lens diverging lens
Converging lenses bring parallel rays together at a focal point; diverging lenses spread rays apart as if they came from a focal point.
Thin lens equation 1/f = 1/do + 1/di Same algebra form as the mirror equation.
Magnification m = hi/ho = -di/do Image height compared with object height.
Optical power P = 1/f f in meters gives power in diopters.

Principal Rays for a Converging Lens

  • A ray parallel to the axis refracts through the far focal point.
  • A ray through the near focal point refracts parallel to the axis.
  • A ray through the center of the lens continues nearly straight.

Lens Types

  • Converging lens: positive focal length; can form real or virtual images.
  • Diverging lens: negative focal length; forms virtual upright reduced images for real objects.
Optics in real devices

11. Optical Instruments

Optical instruments use lenses, mirrors, apertures, sensors, and the eye to control image size, brightness, focus, and clarity.

Optical instrument system Optical devices control light path, focus, and image size object aperture lens sensor / retina
Cameras, eyes, microscopes, and telescopes all control ray paths to form useful images at a sensor, retina, or eyepiece.
Instrument Main Optical Idea What Students Should Notice
EyeConverging lens focuses light on retinaRetina receives a real inverted image.
CameraLens focuses light on sensorAperture controls light; focus changes image distance.
MicroscopeMultiple lenses magnify small objectsObjective creates an image enlarged by eyepiece.
TelescopeCollects and magnifies distant lightLarge aperture gathers more light.
Fiber optic cableTotal internal reflectionLight stays trapped inside the core.
GlassesCorrect focal positionConverging or diverging lenses compensate eye focusing errors.
Simulation labs

12. Simulation Labs for This Unit

These official PhET simulations help students visualize reflection, refraction, ray tracing, lens/mirror images, color mixing, and optical behavior.

Optics simulation workflow Use simulations to connect ray diagrams with measurements Change index, angle, object distance Measure ray angle, image distance Explain use Snell or lens equations A strong simulation answer includes a ray sketch, measurements, and formula support.
Optics simulations are strongest when students compare predicted ray diagrams with measured image positions and angles.
Bending Light

Explore refraction, reflection, Snell's law, critical angle, prisms, and how light changes direction between media.

Lab idea: change the material pair and measure how the refraction angle changes.
Open Simulation
Geometric Optics

Move objects, lenses, mirrors, and screens to study real images, virtual images, focal length, and magnification.

Lab idea: place an object outside 2f, at 2f, between f and 2f, and inside f.
Open Simulation
Geometric Optics: Basics

Use a simpler ray-tracing environment to build confidence with lenses, mirrors, images, and focal points.

Lab idea: predict image direction and size before turning on ray lines.
Open Simulation
Color Vision

Investigate red, green, and blue light, white light, filters, perceived color, and how eyes detect color.

Lab idea: mix red, green, and blue light, then compare additive and subtractive color behavior.
Open Simulation
Investigation skills

13. Light and Optics Lab Skills

Optics labs require careful alignment. Small angle errors, poor lens placement, and measuring from the wrong reference point can change results significantly.

Optical bench measurements Measure distances from the lens or mirror reference point do di object lens screen
Optics lab accuracy depends on alignment, using the correct reference point, and measuring object and image distances consistently.

Common Labs

  • Law of reflection lab using plane mirrors and ray boxes.
  • Snell's law lab using acrylic blocks or water tanks.
  • Critical angle and total internal reflection lab.
  • Focal length measurement for converging lenses.
  • Concave mirror image-distance lab.
  • Ray diagram verification using optical benches.
  • Color filters and additive color mixing lab.

Useful Measurements

  • Angles from the normal, not from the surface.
  • Object distance from mirror or lens center.
  • Image distance from mirror or lens center.
  • Focal length in meters or centimeters.
  • Object height and image height.
  • Wavelength or color for dispersion observations.
Lab warning: In lens and mirror labs, always define the reference point for distance measurements before collecting data.
Worked examples

14. Worked Examples

Example 1: Speed of light in glass

Light travels through glass with n = 1.50. Find its speed in glass.

v = c/n = (3.00 × 108)/(1.50) = 2.00 × 108 m/s.

Example 2: Snell's law

Light travels from air into glass. n1 = 1.00, n2 = 1.50, and θ1 = 30°. Find θ2.

n1sinθ1 = n2sinθ2.

sinθ2 = (1.00/1.50)sin30° = 0.333, so θ2 = 19.5°.

Example 3: Critical angle

Find critical angle for glass n = 1.50 to air n = 1.00.

sinθc = n2/n1 = 1.00/1.50 = 0.667.

θc = 41.8°.

Example 4: Wavelength in glass

Light has wavelength 600 nm in vacuum. Find wavelength in glass with n = 1.50.

λglass = λvacuum/n = 600/1.50 = 400 nm.

Example 5: Concave mirror image distance

A concave mirror has f = 12 cm. An object is 36 cm in front of it. Find image distance.

1/f = 1/do + 1/di.

1/12 = 1/36 + 1/di, so 1/di = 1/18 and di = 18 cm.

Example 6: Mirror magnification

Using example 5, find magnification.

m = -di/do = -18/36 = -0.50.

The image is inverted and half the object size.

Example 7: Converging lens

A converging lens has f = 10 cm. An object is 30 cm from the lens. Find image distance.

1/10 = 1/30 + 1/di, so 1/di = 1/15 and di = 15 cm.

Example 8: Lens magnification

Using example 7, find magnification.

m = -di/do = -15/30 = -0.50.

The image is real, inverted, and reduced.

Example 9: Optical power

A lens has focal length 0.25 m. Find optical power.

P = 1/f = 1/0.25 = 4.0 diopters.

Example 10: Reflection angle

A ray hits a mirror at 40° from the normal. Find reflected angle.

θr = θi = 40° from the normal.

Independent practice

15. Practice Problems

Try each problem first. Then open the answer check and compare formulas, signs, units, and ray-diagram reasoning.

1. Find the frequency of red light with wavelength 650 nm in vacuum.

Answer

f = c/λ = (3.00 × 108)/(650 × 10-9) = 4.62 × 1014 Hz.

2. Light travels in water with n = 1.33. Find its speed.

Answer

v = c/n = (3.00 × 108)/1.33 = 2.26 × 108 m/s.

3. A ray hits a mirror at 25° from the normal. What is the angle of reflection?

Answer

25° from the normal.

4. A plane mirror has an object 2.0 m in front of it. Where is the image?

Answer

2.0 m behind the mirror, virtual and upright.

5. Light goes from air into water. n1 = 1.00, n2 = 1.33, θ1 = 45°. Find θ2.

Answer

sinθ2 = (1.00/1.33)sin45° = 0.532, so θ2 = 32.1°.

6. Light moves from glass n = 1.50 to air n = 1.00. Find critical angle.

Answer

sinθc = 1.00/1.50 = 0.667, so θc = 41.8°.

7. Why does light bend toward the normal when entering glass from air?

Answer

Glass has higher refractive index, so light slows down and bends toward the normal.

8. A 500 nm light wave enters glass n = 1.50. Find wavelength in glass.

Answer

λglass = 500/1.50 = 333 nm.

9. What happens to frequency when light enters a new medium?

Answer

Frequency stays the same. Speed and wavelength change.

10. A concave mirror has radius 40 cm. Find focal length.

Answer

f = R/2 = 40/2 = 20 cm.

11. A concave mirror has f = 15 cm and object distance 45 cm. Find image distance.

Answer

1/15 = 1/45 + 1/di, so 1/di = 2/45 and di = 22.5 cm.

12. Using problem 11, find magnification.

Answer

m = -di/do = -22.5/45 = -0.50.

13. A converging lens has f = 20 cm and object distance 60 cm. Find image distance.

Answer

1/20 = 1/60 + 1/di, so 1/di = 1/30 and di = 30 cm.

14. Using problem 13, find magnification.

Answer

m = -30/60 = -0.50. The image is inverted and reduced.

15. A lens has f = -25 cm. Is it converging or diverging?

Answer

Diverging lens because focal length is negative.

16. A lens has focal length 0.50 m. Find optical power.

Answer

P = 1/f = 1/0.50 = 2.0 diopters.

17. Which bends more in a glass prism: red light or violet light?

Answer

Violet light usually bends more because glass has a slightly higher index for shorter wavelengths.

18. What optical principle keeps light inside a fiber optic cable?

Answer

Total internal reflection.

19. What kind of image does a convex mirror form for a real object?

Answer

Virtual, upright, and reduced.

20. In the Bending Light simulation, what should happen when the incident angle exceeds the critical angle from glass to air?

Answer

Total internal reflection occurs, so the ray reflects back into the glass instead of refracting into air.

Final review

16. What to Know Before Moving On

  • Light is an electromagnetic wave and travels at c = 3.00 × 108 m/s in vacuum.
  • The wave equation for light is c = fλ in vacuum.
  • Index of refraction is n = c/v.
  • Reflection obeys θi = θr.
  • Refraction occurs because light changes speed in a new medium.
  • Snell's law is n1sinθ1 = n2sinθ2.
  • Total internal reflection occurs only from higher n to lower n above the critical angle.
  • Dispersion separates white light because refractive index depends on wavelength.
  • Plane mirrors form virtual, upright, same-size images.
  • Concave mirrors and converging lenses can form real inverted images.
  • Mirror and lens calculations use 1/f = 1/do + 1/di.
  • Magnification is m = -di/do.
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