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Optics - Wave Optics (Huygens' Principle)

Grade 12ICSEPhysics

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A wavefront is defined as the locus of all points in a medium which are vibrating in the same phase at a given instant.

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Huygens' Principle states that every point on a given wavefront (primary wavefront) acts as a source of secondary wavelets, which spread out in all directions with the speed of light.

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The new wavefront at a later time is the forward envelope (the tangential surface) of the secondary wavelets.

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Types of wavefronts: A point source produces a spherical wavefront, a linear source produces a cylindrical wavefront, and a source at infinity produces a plane wavefront.

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During refraction, when a wave travels from one medium to another, its frequency ff remains constant, but its speed vv and wavelength λ\lambda change.

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According to Huygens' construction, light travels slower in a denser medium, which leads to the derivation of Snell's Law: sin⁡isin⁡r=v1v2=n21\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = n_{21}.

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A plane wavefront incident on a convex lens emerges as a converging spherical wavefront, while incident on a concave lens, it emerges as a diverging spherical wavefront.

📐Formulae

v=fλv = f \lambda

n=cvn = \frac{c}{v}

n21=n2n1=v1v2=λ1λ2n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}

sin⁡isin⁡r=v1v2\frac{\sin i}{\sin r} = \frac{v_1}{v_2}

λmedium=λairn\lambda_{medium} = \frac{\lambda_{air}}{n}

💡Examples

Problem 1:

Monochromatic light of wavelength 589 nm589 \text{ nm} is incident from air on a water surface. If the refractive index of water is 1.331.33, find the wavelength and speed of light in water. (Given c=3×108 m/sc = 3 \times 10^8 \text{ m/s})

Solution:

  1. Speed in water: v=cn=3×1081.33≈2.25×108 m/sv = \frac{c}{n} = \frac{3 \times 10^8}{1.33} \approx 2.25 \times 10^8 \text{ m/s}.
  2. Wavelength in water: λwater=λairn=589 nm1.33≈442.86 nm\lambda_{water} = \frac{\lambda_{air}}{n} = \frac{589 \text{ nm}}{1.33} \approx 442.86 \text{ nm}.

Explanation:

The frequency of light remains the same when moving between media. The speed and wavelength decrease in a medium with a higher refractive index by a factor of nn.

Problem 2:

Explain the shape of the wavefront when a plane wavefront is reflected by a concave mirror.

Solution:

When a plane wavefront is incident on a concave mirror, the different parts of the wavefront reach the mirror at different times. The center of the wavefront hits the deepest part of the mirror last. Upon reflection, the wavefront becomes a converging spherical wavefront centered at the focus FF.

Explanation:

According to Huygens' Principle, each point on the mirror acts as a secondary source. The path difference created by the curvature of the mirror transforms the plane wavefront into a spherical one.

Wave Optics (Huygens' Principle) - Revision Notes & Key Formulas | ICSE Class 12 Physics