Wave Optics

Wave OpticsNEET Physics · Class 12 · NCERT Chapter 10

Overview Notes NEET Questions Interactive Learning

8 interactive concept widgets for Wave Optics. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Huygens wavefront animation

Resultant intensity from two coherent sources

Young's double slit fringe simulator

Fringe shift with a glass slab

Single-slit diffraction pattern

Resolving power of telescope and microscope

Brewster's angle (polarisation by reflection)

Malus' law: intensity through a polariser

Wavefronts and superposition

Build the new wavefront from secondary wavelets, then add up two coherent waves at a point.

Huygens principle

Huygens wavefront animation

Watch wavefronts expand from a point source or move forward as a plane wave.

Each wavefront is the envelope of secondary wavelets from points on the previous wavefront. Watch the wavefronts expand outward at constant speed.

Animation speed: 0.04

Try this

Spherical wavefronts: from a nearby point source. Curvature decreases at large distances.
Plane wavefronts: from a very distant source (like a star). Sun gives nearly plane wavefronts on Earth.
Each point on the front spawns wavelets; their envelope is the next front. Reflection and refraction are derived from this idea.
Set animation speed to 0 to freeze a snapshot.

Interference intensity

Resultant intensity from two coherent sources

Adjust intensities and path difference; see how the resultant changes.

Two coherent sources of intensity I_1 and I_2 give a resultant intensity that depends on the phase difference between them.

I_1: 4.0 units

I_2: 1.0 units

Path difference Δx: 0.50 λ (φ = 180°)

Resultant intensity I

1.00 units

I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ

I_max

9.00

I_min

1.00

Fringe visibility: 0.80

Try this

Δx = 0 or λ: I = I_1 + I_2 + 2√(I_1 I_2) (constructive). Equal sources: I_max = 4 I_0.
Δx = λ/2: I = I_1 + I_2 - 2√(I_1 I_2) (destructive). Equal sources: I_min = 0.
For unequal sources, I_min > 0: total destructive cancellation needs equal amplitudes.
Visibility V = (I_max - I_min)/(I_max + I_min) = 1 only when I_1 = I_2.

Young's double slit experiment

See the fringe pattern react to slit separation, slit-screen distance, wavelength, and an extra glass slab.

YDSE

Young's double slit fringe simulator

See the fringe width respond as you change λ, d or D.

Drag any slider; the bright fringes get closer or farther. Fringe width β = λD / d.

Wavelength λ: 550 nm

Slit separation d: 0.50 mm

Slit to screen D: 1.50 m

Fringe width β

1.650 mm

β = \frac{λ D}{d}

n-th bright at x = nβ. n-th dark at (n + 1/2)β.

Try this

Halving d doubles the fringe width: fringes spread out.
Doubling D doubles the fringe width: same effect, different lever.
Red light (700 nm) gives wider fringes than blue (450 nm) for the same setup.
Immersing the apparatus in water changes effective λ to λ/n; fringes shrink by factor n.

YDSE fringe shift

Fringe shift with a glass slab in front of one slit

A thin slab adds extra optical path; the whole pattern shifts.

Adding a glass slab in front of one slit shifts the whole pattern towards that slit by an amount proportional to the extra optical path (n - 1) t.

λ: 550 nm

d: 0.50 mm

D: 1.50 m

Glass index n: 1.50

Slab thickness t: 20 µm

Fringe shift

30.000 mm

Δ y = \frac{( n - 1 ) t D}{d}

Fringes shifted

18.18 fringes

= (n − 1) t / λ

Fringe width β = 1.650 mm (unchanged)

Try this

The fringe width itself does not change. Only the position of the central max shifts.
For glass (n = 1.5) and t = 10 µm, λ = 500 nm: shift is (0.5 × 10 µm) / 500 nm = 10 fringes.
Direction of shift: towards the slit covered by the slab. Light through that slit is delayed.
You can use this shift to measure the index n if t is known precisely.

Diffraction and resolving power

Single-slit diffraction width and the angular limit of telescopes and microscopes.

Single-slit diffraction

Single-slit diffraction pattern

See the central maximum widen as the slit narrows.

Diffraction at a single slit gives a bright central maximum twice as wide as the side maxima. Slit minima: a sin θ = nλ.

λ: 550 nm

Slit width a: 20 µm

D: 1.50 m

Width of central maximum

82.500 mm

Width = \frac{2 λ D}{a}

sin θ at first minimum

2.75e-2 (1.58°)

Try this

Narrower slit → wider central max. The diffraction effect is bigger when the opening is comparable to λ.
Width of central max is twice the spacing between consecutive secondary minima.
Compared to YDSE: in YDSE all bright fringes equal in brightness; here the central is much brighter than the rest.
A 50 µm slit lit by 600 nm light at D = 1.5 m: central max width = 36 mm.

Resolving power

Resolving power of a telescope and microscope

Pick the instrument and see how aperture and wavelength set the limit.

Two close objects look distinct only when their angular separation exceeds the resolving limit. Bigger aperture or shorter wavelength gives finer detail.

λ: 550 nm

Aperture D: 100 mm

Angular resolution Δθ

1.38″

Δ θ = \frac{1.22 λ}{D}

Resolving power = 1 / Δθ

Try this

Hubble has a 2.4 m mirror; 550 nm light → Δθ = 0.05 arcsec.
Compound microscope with NA = 1.0 and λ = 550 nm: best resolution ≈ 275 nm.
UV microscopes (λ = 250 nm) push resolution into 100 nm range. Electron microscopes use λ ≈ 1 pm.
Larger aperture or NA → better resolution. That is why bigger telescopes see finer detail.

Polarisation: Brewster and Malus

Brewster's angle for full polarisation by reflection, and Malus' cos² law for a polariser pair.

Brewster's angle

Brewster's angle (polarisation by reflection)

Set the medium and read the angle at which reflected light is fully polarised.

At Brewster's angle, the reflected ray is fully plane-polarised (perpendicular to plane of incidence) and the reflected and refracted rays are perpendicular to each other.

Refractive index n: 1.50

Brewster's angle θ_B

56.31°

tan θ_{B} = n

Angle of refraction at θ_B

33.69°

θ_B + θ_r = 90°

Try this

For glass-air (n = 1.5): θ_B ≈ 56.3°. Above this, sky glare reflects from horizontal glass surfaces.
For water (n = 1.33): θ_B ≈ 53°. Polaroid sunglasses block polarised glare from water.
Reflected and refracted rays are perpendicular only at Brewster's angle.
Brewster's law assumes the incident light is from the rarer side (e.g. air to glass).

Malus' law

Malus' law: intensity through a polariser

Adjust the angle and see the cos² fall-off.

Already polarised light passing through a polariser at angle θ has intensity I = I_0 cos² θ. At 90° (crossed), no light passes.

Angle θ between axes: 30°

Incoming polarised I_0: 100 W/m²

Transmitted intensity

75.00 W/m²

That is 75.0% of I_0.

I = I_{0} cos^{2} θ

Try this

Theta = 0: full transmission (parallel polarisers).
Theta = 90°: zero transmission (crossed polarisers).
Theta = 60°: I = I_0 / 4. Theta = 45°: I = I_0 / 2.
Unpolarised → ideal polariser: half intensity (because cos² averaged over all angles is 1/2).

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