Wave Optics Notes
Study Notes
Topics
4Chapter Overview
Overview
Wave optics explains optical phenomena that cannot be understood fully by treating light only as straight rays. It studies light as a wave and explains Huygens principle, interference, diffraction and polarisation. Huygens principle says every point on a wavefront acts as a source of secondary wavelets, helping derive reflection and refraction. Interference explains redistribution of intensity when coherent waves superpose, especially in Young’s Double Slit Experiment. Diffraction shows bending and spreading of light around obstacles or through narrow apertures. Polarisation proves that light is transverse because only transverse waves can be plane polarised. For NEET, the most important areas are fringe width, coherent sources, single-slit pattern, Brewster’s law and conceptual comparisons.
- 1Ray is always perpendicular to the wavefront in an isotropic medium.
- 2Interference redistributes energy; it does not destroy energy.
- 3In YDSE, bright and dark fringes are equally spaced under standard approximations.
- 4Diffraction depends strongly on aperture width.
- 5Central maximum in single-slit diffraction is twice as wide as secondary maxima.
- 6Polarisation cannot occur for longitudinal waves.
- 7Unpolarised light has vibrations in all planes perpendicular to direction of propagation.
Chapter Order Trick
Remember W-I-D-P: Wavefront first, Interference next, Diffraction after aperture, Polarisation proves transverse nature.
NEET Formula Priority
For scoring quickly, revise β = λD/d, a sin θ = nλ and tan iB = μ before solving PYQs.
Everyday Wave Optics
Colourful soap bubbles show interference, spreading of light around a sharp edge shows diffraction, Polaroid sunglasses use polarisation, and Huygens principle explains how a wavefront moves forward.
Mixing Ray Optics and Wave Optics
Ray optics explains reflection and refraction using rays, but interference, diffraction and polarisation require the wave nature of light.
Ignoring Units
Convert wavelength from nm or Å to metre before using β = λD/d or v = fλ.
Relates speed, frequency and wavelength of a wave.
Variables
v=wave speed in m/s
f=frequency in Hz
λ=wavelength in metre
Distance between two consecutive bright or dark fringes in Young’s Double Slit Experiment.
Variables
β=fringe width
λ=wavelength of light
D=distance between slits and screen
d=separation between the two slits
Huygens Principle
Overview
Huygens principle is a geometrical method to describe wave propagation. A wavefront is a surface on which all particles vibrate in the same phase. Every point on a wavefront acts as a source of secondary spherical wavelets, and the new wavefront at a later time is the forward envelope of these wavelets. Rays are perpendicular to wavefronts in homogeneous isotropic media. Plane wavefronts come from very distant sources, spherical wavefronts come from point sources, and cylindrical wavefronts come from line sources. Using wavefront construction, laws of reflection and refraction can be derived. In refraction, bending occurs because wave speed changes in the second medium.
- 1Huygens principle supports the wave nature of light.
- 2Secondary wavelets spread with the speed of light in that medium.
- 3Only the forward envelope is considered physically effective in elementary treatment.
- 4In reflection, incident and reflected wavefronts make equal angles with the reflecting surface.
- 5In refraction, change of wave speed changes wavelength but frequency remains same.
- 6When light enters a denser medium, wavefront spacing decreases because speed decreases.
Wavefront Definition Trick
Wavefront means 'same phase front'. If particles are vibrating together in phase, they lie on the same wavefront.
Ray Direction Trick
Ray is the arrow; wavefront is the wall. The arrow always hits the wall at 90° in a uniform isotropic medium.
Sunlight Example
Sun is very far from Earth, so the small portion of sunlight reaching a laboratory can be treated as a plane wavefront.
Water Ripple Example
A stone dropped in still water creates circular wavefronts. Each point on a ripple can be imagined as producing tiny secondary ripples.
Calling Wavefront a Ray
A ray shows direction of energy propagation, while a wavefront is a surface of equal phase. They are related but not identical.
Changing Frequency in Refraction
During refraction, frequency remains constant. Speed and wavelength change according to the medium.
Forgetting Medium Dependence
Secondary wavelets travel with the speed of light in that particular medium, not always with speed c.
Used to connect propagation speed of a wavefront with frequency and wavelength.
Variables
v=wave speed
f=frequency
λ=wavelength
A medium with lower wave speed has higher refractive index.
Variables
μ=absolute refractive index
c=speed of light in vacuum
v=speed of light in the medium
Interference
Overview
Interference is the redistribution of light intensity when two or more coherent waves superpose. According to the principle of superposition, the resultant displacement at a point is the algebraic sum of individual displacements. In Young’s Double Slit Experiment, a single source illuminates two narrow slits, making them coherent secondary sources. Their waves overlap on a screen to produce alternate bright and dark fringes. Bright fringes occur when path difference is an integral multiple of wavelength, while dark fringes occur when path difference is an odd multiple of half wavelength. Fringe width depends directly on wavelength and screen distance, and inversely on slit separation. YDSE is one of the most important NEET numericals.
- 1Interference does not violate conservation of energy; energy is redistributed from dark regions to bright regions.
- 2Two independent ordinary bulbs do not produce sustained interference because they are not coherent.
- 3In YDSE, slit width should be small and separation should be much smaller than screen distance.
- 4Increasing wavelength increases fringe width.
- 5Increasing slit separation decreases fringe width.
- 6If the whole YDSE setup is immersed in a medium, wavelength decreases and fringe width decreases.
Bright-Dark Path Difference
Bright is Whole λ: Δx = nλ. Dark is Half-odd λ: Δx = (2n + 1)λ/2.
Fringe Width Dependence
β loves λ and D, hates d: β = λD/d. Bigger wavelength or screen distance widens fringes; bigger slit separation narrows them.
Wave Speed Numerical Example
If frequency f = 2 Hz and wavelength λ = 3 m, then v = fλ = 2 × 3 = 6 m/s. Here f is in Hz, λ is in m and v is in m/s.
YDSE Numerical Example
In YDSE, λ = 600 nm, D = 2 m and d = 0.5 mm. β = λD/d = (600 × 10^-9 × 2)/(0.5 × 10^-3) = 2.4 × 10^-3 m = 2.4 mm.
Real-Life Example
The colours seen in thin soap films arise due to interference between light reflected from the top and bottom surfaces of the film.
Using Non-Coherent Sources
Stable interference is not obtained from two independent ordinary light sources because their phase difference changes randomly.
Confusing Fringe Width with Fringe Position
Fringe width β is the separation between consecutive fringes. Position yn is measured from the central maximum.
Forgetting Unit Conversion
Wavelength is often given in nm. Convert 600 nm to 600 × 10^-9 m before using β = λD/d.
Basic wave formula. Example: if f = 2 Hz and λ = 3 m, then v = fλ = 2 × 3 = 6 m/s.
Variables
v=wave speed in m/s
f=frequency in Hz
λ=wavelength in m
Condition for bright fringe when waves arrive in phase.
Variables
Δx=path difference
n=integer order 0, 1, 2, 3...
λ=wavelength
Condition for dark fringe when waves arrive in opposite phase.
Variables
Δx=path difference
n=integer order 0, 1, 2, 3...
λ=wavelength
Diffraction
Overview
Diffraction is the bending and spreading of light when it passes through a narrow aperture or around an obstacle. It becomes prominent when the size of the aperture or obstacle is comparable to the wavelength of light. In single-slit diffraction, different parts of the same wavefront act as secondary sources and interfere with one another. The pattern consists of a broad and bright central maximum, followed by weaker secondary maxima on both sides separated by dark minima. The first minima satisfy a sin θ = ±λ. Unlike YDSE interference fringes, single-slit diffraction fringes are not equally bright, and the central maximum is twice as wide as the secondary maxima.
- 1Diffraction proves that light has wave nature.
- 2A very wide aperture produces negligible diffraction and light appears to travel almost straight.
- 3Decreasing slit width increases spreading of the diffraction pattern.
- 4The central maximum extends between first minima on both sides.
- 5Intensity of secondary maxima decreases as order increases.
- 6Diffraction and interference are both based on superposition but differ in source arrangement.
Diffraction Condition
Diffraction is clearly visible when slit size and wavelength are close friends: a ≈ λ.
Central Maximum
In diffraction, Central is Champion: brightest and widest. Secondary maxima are smaller side players.
Numerical Example
Light of wavelength 600 nm passes through a slit of width 0.3 mm. For first minimum, sin θ = λ/a = 600 × 10^-9 / 0.3 × 10^-3 = 2 × 10^-3, so θ ≈ 0.002 rad.
Real-Life Example
Light spreading around the edge of a blade or through a tiny gap shows diffraction, though it is less obvious than water-wave diffraction because light wavelength is very small.
Thinking Diffraction Needs Two Slits
Diffraction can occur with a single slit. Interference in YDSE uses two coherent slits.
Using Bright Condition for Minima
For single-slit diffraction, dark minima occur at a sin θ = nλ. This looks like constructive condition in YDSE, so do not mix them.
Assuming All Maxima Are Equal
In diffraction, secondary maxima have decreasing intensity. Only the central maximum is strongest.
Condition for dark fringes in single-slit diffraction.
Variables
a=slit width
θ=angle of diffraction
n=order of minimum, n = 1, 2, 3...
λ=wavelength of light
Small-angle angular width between first minima on both sides of central maximum.
Variables
λ=wavelength of light
a=slit width
Polarisation
Overview
Polarisation is the phenomenon in which vibrations of light are restricted to a particular plane perpendicular to the direction of propagation. Ordinary light is unpolarised because its electric field vibrations occur randomly in all possible transverse directions. When only one vibration direction remains, the light is plane polarised. Since longitudinal waves cannot be polarised, polarisation proves that light is transverse in nature. Light can be polarised by selective absorption using Polaroids, by reflection, by scattering and by double refraction in some crystals. At Brewster’s angle, reflected light is completely plane polarised, and the reflected and refracted rays are perpendicular. Applications include Polaroid sunglasses, photography, LCDs and stress analysis.
- 1Only transverse waves can be polarised.
- 2In electromagnetic light waves, electric field vibrations are considered for polarisation.
- 3A polariser converts unpolarised light into plane polarised light.
- 4An analyser is used to test whether light is polarised.
- 5When polariser and analyser axes are parallel, transmitted intensity is maximum.
- 6When their axes are crossed at 90°, transmitted intensity is minimum or zero for ideal Polaroids.
- 7Polarisation by reflection is strongest at Brewster’s angle.
Polarisation Proof
P for Polarisation, P for Perpendicular vibrations: only transverse waves have vibrations perpendicular to motion, so only they can be polarised.
Brewster Memory
Brewster makes a right angle: at iB, reflected and refracted rays are 90° apart, and tan iB = μ.
Brewster Angle Example
For glass with μ = 1.5, tan iB = 1.5. Thus iB ≈ 56.3°. At this angle, reflected light is completely plane polarised.
Malus Law Example
If plane polarised light of intensity I0 passes through an analyser at 60°, transmitted intensity is I = I0 cos²60° = I0/4.
Real-Life Example
Polaroid sunglasses reduce glare from roads, water and glass because reflected glare is often partially plane polarised.
Saying Sound Can Be Polarised
Sound in air is longitudinal, so it cannot be polarised. Polarisation is evidence that light is transverse.
Confusing Plane of Vibration and Plane of Polarisation
In many school texts, plane of polarisation is perpendicular to the plane of vibration. NEET usually focuses on transmitted vibration direction through Polaroids.
Using sin Instead of tan in Brewster’s Law
Brewster’s law is tan iB = μ, not sin iB = μ.
Forgetting Half Intensity
Unpolarised light passing through an ideal polariser becomes plane polarised with intensity I0/2.
Gives the angle of incidence at which reflected light becomes completely plane polarised.
Variables
iB=Brewster angle or polarising angle
μ=refractive index of reflecting medium with respect to incident medium
At Brewster’s angle, reflected and refracted rays are mutually perpendicular.
Variables
iB=Brewster angle
r=angle of refraction at Brewster incidence
Formula Sheet
10Relates speed, frequency and wavelength of a wave.
Variables
v=wave speed in m/s
f=frequency in Hz
λ=wavelength in metre
Distance between two consecutive bright or dark fringes in Young’s Double Slit Experiment.
Variables
β=fringe width
λ=wavelength of light
D=distance between slits and screen
d=separation between the two slits
Condition for dark bands in single-slit diffraction.
Variables
a=width of slit
θ=angle of diffraction
n=order of minimum, n = 1, 2, 3...
λ=wavelength of light
Gives the polarising angle for polarisation by reflection.
Variables
iB=Brewster angle or polarising angle
μ=refractive index of reflecting medium with respect to incident medium
Used to connect propagation speed of a wavefront with frequency and wavelength.
Variables
v=wave speed
f=frequency
λ=wavelength
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NEET PYQs — Wave Optics
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In Young’s double slit experiment, using monochromatic light of wavelength λ, the intensity of light at a point on the screen where the path difference is λ is K units. The intensity of light at a point where the path difference is λ/3 will be:
Two slits in Young's experiment have widths in the ratio $1:25$. The ratio of intensity at the maxima and minima in the interference pattern, $\dfrac{I_{\max}}{I_{\min}}$, is:
In Young's double slit experiment, the slits are $2\,\text{mm}$ apart and are illuminated by photons of wavelengths $\lambda_1=12000\,\text{Å}$ and $\lambda_2=10000\,\text{Å}$. At what minimum distance from the common central bright fringe on a screen $2\,\text{m}$ from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?
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