**Definition of Wavefront:** A wavefront is a surface of constant phase where all points oscillate in phase. It is the locus of points that vibrate with the same amplitude and phase at a given instant. Energy propagates perpendicular to the wavefront.
**Types of Wavefronts:**
**Huygens Principle Statement:** Each point on a wavefront acts as a source of secondary wavelets that spread out with the speed of the wave in that medium. The envelope of all secondary wavelets gives the new wavefront position at a later time.
**Application of Huygens Construction:**
**Important Observations:**
**Exam Point:** Huygens principle is purely geometric; it does not explain wave mechanism but provides practical method to determine wavefront evolution. This principle successfully explains reflection, refraction, diffraction, and interference phenomena.
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**Derivation of Snell's Law:**
Consider a plane wavefront AB incident at angle i on interface PP' separating medium 1 (wave speed v₁) and medium 2 (wave speed v₂).
**Step-by-Step Derivation:**
1) Let time t be taken for wavefront to travel distance BC, then:
**BC = v₁t** (distance traveled in medium 1)
2) From point A (on the interface), draw a sphere of radius v₂t in medium 2
3) Draw tangent plane CE from point C to this sphere. The refracted wavefront is CE, where:
**AE = v₂t** (distance traveled in medium 2 in same time t)
4) In triangle ABC:
**sin i = BC/AC = v₁t/AC** ... (equation 10.1)
5) In triangle AEC:
**sin r = AE/AC = v₂t/AC** ... (equation 10.2)
6) Dividing equations:
**sin i/sin r = v₁/v₂** ... (equation 10.3)
**Refractive Index Definition:**
where c is speed of light in vacuum
**Snell's Law (Final Form):**
**n₁ sin i = n₂ sin r** ... (equation 10.6)
**Key Insight from Wave Theory:** If the ray bends toward normal (r < i), then v₂ < v₁. This means light travels slower in the denser medium. This contradicts corpuscular theory but was confirmed experimentally by Foucault (1850).
**Wavelength Change During Refraction:**
When BC = λ₁ (wavelength in medium 1), then AE = λ₂ (wavelength in medium 2) because the wave crest that reaches C also reaches E in time t.
**λ₁/λ₂ = v₁/v₂** ... (equation 10.7)
This shows:
**Example Problem:**
Light traveling in air (n₁ = 1.0) enters glass (n₂ = 1.5) at incident angle 30°. Find refraction angle and wavelength change (given λ₀ = 600 nm in air).
**Solution:**
Using Snell's law: n₁ sin i = n₂ sin r
1.0 × sin 30° = 1.5 × sin r
1.0 × 0.5 = 1.5 × sin r
sin r = 0.333
**r = 19.47°** (ray bends toward normal in denser medium)
For wavelength: λ₂ = λ₁ × (v₂/v₁) = λ₁ × (n₁/n₂)
λ₂ = 600 nm × (1.0/1.5) = **400 nm** in glass
---
**Critical Angle Definition:** When light travels from denser to rarer medium, the critical angle i_c is the incident angle at which refraction angle becomes 90°.
**Critical Angle Formula:**
**sin i_c = n₂/n₁** ... (equation 10.8)
where n₁ > n₂ (light traveling from denser to rarer medium)
**Derivation:** Using Snell's law when r = 90°:
n₁ sin i_c = n₂ sin 90°
n₁ sin i_c = n₂ × 1
**sin i_c = n₂/n₁**
**Total Internal Reflection (TIR):**
**Conditions for TIR:**
1) Light must travel from denser to rarer medium
2) Incident angle must exceed critical angle: i > i_c
3) Reflected intensity equals incident intensity (100% reflection)
**Practical Application - Optical Fibres:**
**Numerical Example:**
Find critical angle for light traveling from glass (n = 1.5) to air (n = 1.0).
sin i_c = 1.0/1.5 = 0.667
**i_c = 41.8°**
This means any light hitting glass-air interface at angle greater than 41.8° will undergo TIR.
---
**Law of Reflection Derivation:**
Consider plane wave AB incident at angle i on reflecting surface MN.
**Construction Steps:**
1) Distance traveled by wavefront: **BC = vt** (in time t)
2) From point A, draw sphere of radius vt. Draw tangent CE from point C to this sphere
3) Thus: **AE = BC = vt**
4) Consider triangles EAC and BAC:
5) Triangles are congruent, therefore: **angle CAE = angle BCA**
This means: **Angle of incidence = Angle of reflection** (i = r)
**Law of Reflection Statement:** The incident ray, reflected ray, and normal all lie in the same plane. The angle of incidence equals the angle of reflection, measured from the normal to the surface.
**Wavefront Behavior in Optical Elements:**
**Prism:** Plane wave passing through prism experiences different delays at different heights because light travels slower in glass. Lower portion (passing through more glass) gets delayed more, tilting the wavefront. This tilt causes ray bending and angular deviation.
**Convex Lens:** Plane wavefront incident on lens gets maximum delay at center (thickest part). Central portion depressed, creating converging spherical wavefront that focuses at focal point F. The delay difference between center and edge exactly converts plane to spherical wavefront.
**Concave Mirror:** Plane wave reflects and develops curvature. By Huygens principle on reflection, the wavefront becomes spherical and converges to focal point F.
**Optical Path Length Principle:** The optical path length (product of refractive index and geometric path length) is equal for all rays reaching the same image point, even though geometric paths differ. This is why a ray through lens center (shorter path in glass but traverses glass) takes same time as edge rays (longer air path) to reach image.
---
**Coherent Sources Definition:** Two sources are coherent if the phase difference between their displacements remains constant with time. They oscillate with same frequency and constant phase relationship.
**Example:** Two needles S₁ and S₂ oscillating identically in water produce coherent sources.
**Condition for Coherence:** Path difference between two sources to an observation point P must be constant (or integer multiples of wavelength).
**Constructive Interference Condition:**
**Path difference Δ = nλ** where n = 0, 1, 2, 3... (integer)
**Phase difference = 2πn** (even multiple of π)
When S₁P = S₂P:
**Maximum intensity I_max = (A₁ + A₂)²** where A₁, A₂ are individual amplitudes
**Physical Explanation:** Crests align with crests and troughs with troughs, producing maximum displacement.
**Destructive Interference Condition:**
**Path difference Δ = (n + ½)λ** where n = 0, 1, 2, 3... (odd multiple of λ/2)
**Phase difference = (2n + 1)π** (odd multiple of π)
When S₂R - S₁R = 2.5λ:
**Minimum intensity I_min = (A₁ - A₂)²**
**Physical Explanation:** Crests of one wave align with troughs of other, causing cancellation.
**Fringe Pattern:** Alternate bright and dark bands formed on screen where bright fringes correspond to constructive interference and dark fringes to destructive interference.
**Exam Point:** Intensity is NOT additive for coherent waves. Simply adding I₁ + I₂ is incorrect; must use vector addition of amplitudes considering phase difference.
---
**Experimental Setup:**
Two narrow slits S₁ and S₂ separated by distance d, illuminated by monochromatic light of wavelength λ. Slits act as coherent sources. Interference pattern observed on screen at distance D from slits.
**Path Difference Derivation:**
For a point P on the screen at distance y from center:
**Path difference:** Δ = r₂ - r₁
For small angles (y << D and d << D):
**Δ ≈ (d·y)/D** ... (using binomial approximation)
**Condition for Bright Fringes (Constructive Interference):**
**Δ = nλ** where n = 0, ±1, ±2, ±3...
**(d·y)/D = nλ**
**y_n = nλD/d** (position of nth bright fringe)
**Fringe Width (Distance between consecutive bright or dark fringes):**
**β = λD/d** ... (equation for fringe width)
This is most important formula for CBSE exams. Larger wavelength increases fringe width, larger distance D increases fringe width, smaller slit separation d increases fringe width.
**Intensity Distribution in Young's Double Slit:**
Resultant amplitude at any point: **A = 2a cos(πΔ/λ)** where a is amplitude from each slit
**Resultant intensity:** **I = 4I₀ cos²(πΔ/λ)**
where I₀ is intensity from single slit
At bright fringes (Δ = nλ): I = 4I₀ (maximum)
At dark fringes (Δ = (n+½)λ): I = 0 (minimum)
**Numerical Example:**
Two slits separated by 1 mm are illuminated by light of wavelength 600 nm. Screen is 1 m away. Calculate fringe width.
**β = λD/d = (600 × 10⁻⁹ × 1)/(1 × 10⁻³)**
**β = 600 × 10⁻⁶ m = 0.6 mm**
Find position of 4th bright fringe:
y₄ = 4λD/d = 4 × 600 × 10⁻⁹ × 1/(1 × 10⁻³)
**y₄ = 2.4 × 10⁻³ m = 2.4 mm**
**Coherence and Visibility:**
**Visibility V = (I_max - I_min)/(I_max + I_min)**
For perfectly coherent sources: V = 1 (clear fringes)
For partially coherent or incoherent sources: V < 1 (fringes fade)
**Exam Point:** Young's experiment was historic proof that light is wave phenomenon. The fringe width formula β = λD/d is high-weightage topic appearing in numerical problems.
---
**Definition:** Diffraction is bending of light around obstacles and spreading of light through narrow apertures. It occurs because each point on wavefront acts as secondary source (Huygens-Fresnel principle).
**Single Slit Diffraction Setup:**
Monochromatic plane wave of wavelength λ incident on single slit of width b. Diffraction pattern observed on distant screen.
**Diffraction vs. Interference:**
**Path Difference Analysis for Single Slit:**
Divide slit into two halves, each of width b/2. For a point P on screen at angle θ from normal:
Path difference between ray from top and bottom of slit:
**Δ = b sin θ**
When light from top half cancels light from bottom half:
**Δ = λ/2** or **b sin θ = λ/2**
This gives condition for first dark fringe.
**Conditions for Single Slit Diffraction Minima:**
**b sin θ = nλ** where n = ±1, ±2, ±3... (not n = 0)
**Dark fringe angles:** **sin θ_n = nλ/b**
**Conditions for Single Slit Diffraction Maxima (Approximate):**
**b sin θ = (n + ½)λ** where n = 1, 2, 3... (not for central maximum)
The central maximum is bright fringe at θ = 0.
**Width of Central Maximum:**
For small angles: θ ≈ sin θ = tan θ
Angular width of central maximum: **2θ₁ = 2λ/b** (from first minimum on either side)
**Linear width on screen at distance D:**
**Central fringe width = 2λD/b**
**Important Observation:** Wider the slit (larger b), narrower the central maximum. As slit becomes very wide compared to wavelength, diffraction effect becomes negligible and light travels approximately in straight lines (geometric optics limit).
**Intensity in Single Slit Diffraction:**
**I = I₀ [sin(πb sin θ/λ)/(πb sin θ/λ)]²**
This is sinc function. At central maximum (θ = 0), using L'Hôpital's rule: I = I₀
**Fringe Intensity Pattern:**
**Comparison: Single Slit vs. Double Slit**
Single slit diffraction shows single bright central fringe with secondary maxima and minima around it. Double slit shows multiple equally-spaced bright fringes (interference pattern) modulated by single slit diffraction envelope (each slit's own diffraction pattern).
**Numerical Example:**
Light of wavelength 500 nm passes through single slit of width 0.1 mm. Screen is 1 m away. Find width of central maximum.
**Central width = 2λD/b = 2 × 500 × 10⁻⁹ × 1/(0.1 × 10⁻³)**
**= 10⁻⁶/(10⁻⁴) = 0.01 m = 1 cm**
Find position of first minimum:
sin θ₁ = λ/b = 500 × 10⁻⁹/(0.1 × 10⁻³) = 5 × 10⁻³
For small angle: y₁ = D tan θ₁ ≈ D sin θ₁ = 1 × 5 × 10⁻³ = **0.5 cm**
This confirms central maximum width = 2 × 0.5 = 1 cm.
**Exam Point:** The formula for central maximum width 2λD/b and condition for minima b sin θ = nλ are frequently asked. Diffraction explains why sharp shadows are not formed and why telescope resolution is limited.
---
**Definition of Resolving Power:** Ability of an optical instrument to distinguish between two closely spaced objects.
**Rayleigh Criterion:** Two point objects are just resolved (barely distinguishable) when the central maximum of diffraction pattern of one object falls on the first minimum of the other.
**For Single Slit:**
The angular separation between center and first minimum: **θ = λ/b**
**Minimum angular separation for two objects to be resolved:** **θ_min = λ/b**
**Resolving Power R = 1/θ_min = b/λ**
Larger slit width b improves resolution, smaller wavelength improves resolution.
**For Circular Aperture (like telescope):**
**Minimum resolvable angle = 1.22 λ/D** (where D is aperture diameter)
This appears in telescope theory. The factor 1.22 arises from exact diffraction calculation for circular opening.
**Practical Implication:** Telescopes with larger objective diameter can resolve smaller angular separations. This is why astronomical telescopes have large objective lenses/mirrors.
---
**General Interference Formula:**
When two coherent waves of equal intensity I₀ and amplitudes a interfere with phase difference δ:
**I = I₁ + I₂ + 2√(I₁I₂) cos δ**
For equal intensities (I₁ = I₂ = I₀):
**I = 2I₀(1 + cos δ)** or **I = 4I₀ cos²(δ/2)**
**Relating Phase Difference to Path Difference:**
When path difference is Δ:
**Phase difference δ = 2πΔ/λ**
So intensity formula becomes:
**I = 4I₀ cos²(πΔ/λ)**
**Maximum Intensity:** When cos δ = 1 or δ = 2nπ (n = 0, 1, 2...)
**I_max = 4I₀** (constructive interference)
**Condition: Δ = nλ**
**Minimum Intensity:** When cos δ = -1 or δ = (2n+1)π
**I_min = 0** (destructive interference)
**Condition: Δ = (n + ½)λ**
**Fringe Visibility:**
**V = (I_max - I_min)/(I_max + I_min) = 1** (for equal amplitude coherent sources)
**Practical Coherence - Finite Source Size:**
Natural light sources have finite extension. Light from different parts of source may not maintain constant phase relationship, reducing visibility of fringes. As source size increases, fringe visibility decreases.
---
**Definition:** Diffraction grating is optical device with large number of closely-spaced parallel slits or reflecting surfaces that produce sharp diffraction maxima.
**Grating Spacing:** If N is number of slits in grating element width W:
**Grating spacing d = W/N** (distance between consecutive slits)
**Condition for Principal Maxima:**
When light of wavelength λ is incident normally:
**d sin θ = nλ** where n = 0, ±1, ±2, ±3... (order of maximum)
This is same as double slit condition, but gratings produce very sharp bright lines with dark regions between them.
**Intensity Distribution:**
Central maximum (n = 0) is most intense. Higher order maxima are progressively weaker. For grating with N slits:
**I_max ∝ N²** for principal maxima
**Width of principal maximum ∝ 1/N** (narrower for more slits)
This is why gratings produce very sharp spectral lines compared to double slit.
**Applications in Spectroscopy:**
Different wavelengths diffract at different angles. By measuring diffraction angle, unknown wavelength can be determined:
**λ = (d sin θ)/n**
**Resolving Power of Grating:**
**R = λ/Δλ = nN**
where n is order and N is total number of slits. Gratings can achieve very high resolving power with large N and high orders.
**Numerical Example:**
A diffraction grating has 5000 lines per cm. Find wavelength if second order maximum appears at 30° angle.
d = 1 cm / 5000 = 2 × 10⁻⁴ cm = 2 × 10⁻⁶ m
Using d sin θ = nλ:
λ = (d sin θ)/n = (2 × 10⁻⁶ × sin 30°)/2
λ = (2 × 10⁻⁶ × 0.5)/2 = **5 × 10⁻⁷ m = 500 nm**
---
**Definition:** Polarization is restriction of light wave vibrations to one or few preferred directions perpendicular to propagation direction.
**Unpolarized Light:** Natural light (from sun, incandescent bulbs) has electric field oscillating randomly in all directions perpendicular to propagation.
**Polarized Light:** Light in which electric field oscillates in only one fixed direction (plane of vibration).
**Plane Polarization:** Electric field vector oscillates in fixed plane containing the propagation direction.
**Types of Polarization:**
1. **Linear (Plane) Polarization:** E-vector oscillates in single plane
2. **Circular Polarization:** E-vector rotates while maintaining constant magnitude
3. **Elliptical Polarization:** E-vector traces elliptical path
**Methods of Polarization:**
**Polarization by Absorption (Polarizer):**
**Polarization by Reflection (Brewster's Angle):**
When unpolarized light reflects from surface at specific angle called Brewster's angle θ_B:
**tan θ_B = n₂/n₁**
At this angle, reflected light is completely polarized (perpendicular to plane of incidence).
**Polarization by Double Refraction:**
Certain crystals (like calcite, quartz) have two different refractive indices for two orthogonal polarization directions. Light splits into two perpendicular polarizations traveling at different speeds.
**Malus's Law:**
When polarized light of intensity I₀ passes through polarizer at angle θ to polarization direction:
**I = I₀ cos² θ**
**Application:** If crossed polarizers (θ = 90°), no light passes (I = 0).
**Numerical Example:**
Unpolarized light of intensity 100 W/m² passes through first polarizer. What is transmitted intensity? If second polarizer is placed at 30° to first, what intensity emerges?
After first polarizer: I₁ = 100/2 = **50 W/m²**
After second polarizer: I₂ = 50 × cos² 30° = 50 × (√3/2)² = 50 × 3/4 = **37.5 W/m²**
**Brewster's Angle for Air-Glass Interface:**
tan θ_B = 1.5/1 = 1.5
θ_B = 56.3°
At this angle, reflected light is plane polarized (vibrating perpendicular to page if incident plane is in page).
**Exam Point:** Polarization demonstrates that light is transverse wave (vibrations perpendicular to propagation). Unpolarized to polarized light reduction by factor 1/2 is important principle.
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**Magnifying Power:** The ratio of angle subtended by image at eye to angle subtended by object when placed at least distance of distinct vision (D = 25 cm).
**Microscope Magnification:**
For simple microscope (single lens as magnifier):
**M = 1 + D/f**
where D = 25 cm and f is focal length in cm.
For compound microscope with objective (focal length f₀) and eyepiece (focal length f_e) separated by tube length L:
**Magnifying Power M = (L/f₀) × (D/f_e)**
where:
**Telescope Magnification:**
For astronomical telescope in normal adjustment (image at infinity):
**Magnifying Power M = -f₀/f_e**
where f₀ is objective focal length and f_e is eyepiece focal length.
Negative sign indicates inverted image.
**Tube length = f₀ + f_e** (separation between objective and eyepiece)
**Terrestrial Telescope:**
Uses additional erecting lens to produce upright image. Magnifying power:
**M = -f₀/f_e** (same as astronomical)
But with erecting lens, no negative sign (no inversion).
**Resolving Power of Telescope:**
Minimum angular separation between two objects to be resolved:
**θ_min = 1.22 λ/D**
where D is objective diameter. Larger objective improves resolution.
**Exam Point:** Magnifying power formulas for microscope (M = L/f₀ × D/f_e) and telescope (M = f₀/f_e) are frequently asked. The tube length, focal lengths, and magnifying power relationships must be understood clearly.
---
**Maxwell's Electromagnetic Theory:**
James Clerk Maxwell showed that changing electric field produces changing magnetic field and vice versa, leading to propagation of electromagnetic disturbance even through vacuum.
**Wave Equation for Electromagnetic Waves:**
Maxwell's equations lead to wave equation for electric field component:
**∂²E/∂t² = (1/c²) ∂²E/∂x²**
where c is speed of light. Solving gives wave solution:
**E = E₀ sin(kx - ωt)**
Similarly for magnetic field:
**B = B₀ sin(kx - ωt)**
**Relationship between E and B:**
**E/B = c** (ratio of electric to magnetic field amplitudes equals wave speed)
**Speed of Electromagnetic Waves:**
From Maxwell's equations:
**c = 1/√(ε₀μ₀)**
where ε₀ = 8.85 × 10⁻¹² F/m (permittivity of free space)
μ₀ = 4π × 10⁻⁷ H/m (permeability of free space)
**Numerical Calculation:**
c = 1/√(8.85 × 10⁻¹² × 4π × 10⁻⁷)
c ≈ 3 × 10⁸ m/s (matches measured speed of light!)
This agreement confirmed that light is electromagnetic wave.
**Properties of Electromagnetic Waves:**
1. **Transverse Nature:** Both E and B fields perpendicular to propagation direction and to each other
2. **Speed:** All EM waves travel at speed c in vacuum
3. **Frequency Independent:** Frequency determined by source, not affected by medium change
4. **Energy and Momentum:** Carries both energy (proportional to E² + B²) and momentum (p = E/c)
**Electromagnetic Spectrum (in order of increasing frequency/decreasing wavelength):**
**Displacement Current:**
**Definition:** Time-varying electric field creates "displacement current" in the dielectric, even without actual charge motion.
**Displacement Current Density:**
**I_d = ε₀ dΦ_E/dt**
where Φ_E is electric flux.
**Significance:** Displacement current bridges gap when actual current stops in capacitor. In capacitor between plates, no conduction current but displacement current exists, allowing circuit to be complete.
**Maxwell's Addition to Ampere's Law:**
**∮ B·dl = μ₀(I_c + I_d)**
where I_c is conduction current and I_d is displacement current.
This symmetry between changing E producing B and changing B producing E (Faraday's law) is fundamental to EM wave generation.
**Exam Point:** Displacement current concept and Maxwell's correction to Ampere's law are important. EM waves are transverse, can propagate in vacuum, and electromagnetic theory predicts exactly measured speed of light — strong evidence for wave nature.
---
**Fresnel Diffraction:** More rigorous formulation than simple Huygens principle, incorporating amplitude and phase variation of secondary wavelets.
**Huygens-Fresnel Principle Statement:**
**Difference from Simple Huygens:**
**
Q1. Which scientist experimentally confirmed that the speed of light in water is less than in air, validating the wave model?
Answer: A — Foucault's 1850 experiment directly measured light speed in different media and confirmed wave model's prediction that light is slower in denser media.
Q2. A wavefront is best defined as:
Answer: B — By definition, a wavefront is a surface of constant phase where all points vibrate in phase, not just a geometric boundary.
Q3. According to Huygens Principle, the new wavefront is found by drawing a common tangent to secondary wavelets of radius:
Answer: B — Huygens Principle uses vt as the radius of secondary wavelets, where v is wave speed in the medium and t is time elapsed.
Q4. A plane wave approximation is valid for spherical waves when the observer is:
Answer: C — At large distances, the curvature of a spherical wavefront becomes negligible and a small portion appears flat like a plane wave.
Q5. The corpuscular model predicts that when light refracts toward the normal at an air-water boundary, light speed should:
Answer: A — Corpuscular model incorrectly predicted that bending toward normal implies acceleration in the second medium, opposite to the correct wave model prediction.
Q6. Which of the following is NOT a valid reason why the wave model of light was initially rejected?
Answer: C — The small wavelength of visible light (~0.6 μm) actually SUPPORTED the wave model by allowing ray approximation; it was the other three factors that caused initial rejection.
Q7. In Huygens Principle, why does the backwave not appear even though the mathematical construction predicts one?
Answer: B — Huygens postulated that secondary wavelets have directional amplitude (maximum forward, zero backward) to resolve the backwave paradox.
Q8. Statement I: A wavefront is always perpendicular to the direction of energy propagation (ray direction). Statement II: Secondary wavelets in Huygens Principle are actual physical disturbances from the medium particles. Which is correct?
Answer: B — Statement I is a fundamental definition (ray ⊥ wavefront). Statement II is false because secondary wavelets are mathematical constructs for finding the next wavefront, not physical sources.
Q9. If the wavelength of light is λ and it propagates with speed v, then using Huygens Principle, the time required for a spherical wavefront from a point source to expand by one wavelength is:
Answer: A — Distance = one wavelength λ; speed = v; time = distance/speed = λ/v using the relationship between wave propagation and Huygens construction.
Q10. Maxwell's electromagnetic theory resolved the apparent contradiction in light propagation through vacuum by proposing that:
Answer: C — Maxwell showed that time-varying electric fields produce time-varying magnetic fields and vice versa, allowing wave propagation in vacuum without any physical medium.
Define wavefront in one sentence.
A wavefront is the locus of all points oscillating in the same phase at any given instant.
State Huygens Principle in simple terms.
Each point on a wavefront acts as a source of secondary wavelets, and the envelope of these wavelets forms the new wavefront position.
Why does corpuscular model predict light travels faster in water than air?
Corpuscular model assumes if light bends toward normal on refraction, it must speed up in the denser medium.
What does wave model predict about light speed in water versus air?
Wave model predicts light travels slower in water than in air, which matches experimental observation.
Who experimentally proved light speed is less in water than air and when?
Foucault experimentally confirmed in 1850 that light speed in water is less than in air, supporting the wave model.
What is the wavelength of yellow light approximately?
The wavelength of yellow light is approximately 0.6 micrometers or 600 nanometers.
What is the relationship between a ray and a wavefront?
A ray is the direction of energy propagation and is always perpendicular to the wavefront.
What is a plane wave and when does it occur?
A plane wave occurs at a large distance from the source when a small portion of a spherical wavefront can be approximated as a flat surface.
Why does Huygens Principle have a backwave problem and how was it resolved?
The backwave (wavelet envelope in backward direction) exists mathematically but Huygens assumed secondary wavelets have maximum amplitude forward and zero backward.
State the definition of geometrical optics.
Geometrical optics is the branch of optics that completely neglects the finiteness of wavelength and assumes light travels in straight lines.
State Huygens Principle and explain how it can be used to determine the position of a wavefront at a later time. [2 marks]
Define secondary wavelets and explain the envelope construction. Use the concept that radius of each secondary wavelet = vt.
Explain why the corpuscular model and wave model of light make opposite predictions about the speed of light in water compared to air. Which prediction is correct and why? [5 marks]
For corpuscular model: bending toward normal → speed increases in water. For wave model: bending toward normal → speed decreases in water. Foucault's 1850 experiment confirmed wave model is correct because v_water < v_air; use Snell's law: n = c/v to justify.
Using Huygens Principle, derive the law of reflection for a plane wavefront striking a plane mirror. Show that angle of incidence equals angle of reflection. [6 marks]
Draw a plane mirror with incident wavefront AB at angle θ to mirror. Construct secondary wavelets of radius vt from all points. The tangent to these wavelets (reflected wavefront) makes equal angle on opposite side. Use geometry of right triangles to prove θ_i = θ_r. Show that the reflected wavefront position follows the law of reflection.
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