Estimated time: 56 minutes
CBSE: Class 12
Maharashtra State Board: Class 12
Definition: Ray of Light
- The path along which light travels is called a ray of light.
- A ray is defined as the path of energy propagation in the limit of wavelength tending to zero.
CBSE: Class 12
Maharashtra State Board: Class 12
Definition: Ray Optics or Geometrical Optics
- The study of optical phenomena under the assumption that it travels in a straight line as a ray is called ray optics or geometrical optics, as geometry is used in this study.
- The branch of optics in which one completely neglects the finiteness of the wavelength is called geometrical optics.
CBSE: Class 12
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Definition: Wave Optics
The branch of optics which uses the wave nature of light to explain the optical phenomena is called wave optics.
CBSE: Class 12
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key Points: Nature of Light
- Corpuscular theory (Newton): Light consists of particles called corpuscles that travel in straight lines; it explains reflection but fails to account for the correct speed in denser media.
- Wave theory (Huygens): Light behaves as a wave and accounts for reflection, refraction, interference, diffraction, and polarisation.
- Wave theory correctly states that the speed of light is lower in denser media, so light bends towards the normal.
- Geometrical (ray) optics studies light as straight-line rays; wave optics explains light using its wave nature.
- Dual nature of light: Light exhibits both particle nature (photons) and wave nature under different conditions.
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Key Points: Light as a Wave
- Light is a transverse electromagnetic wave consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.
- Light does not require a medium and travels in a vacuum at the speed of light
c = 3 × 108 m/s
Refractive index n = \[\frac {c}{v}\]
- Visible light has wavelengths from 400–700 nm; different wavelengths produce different colours and cause dispersion (spectrum formation).
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Key Points: Light Sources and Wavefronts
- Primary sources emit their own light (e.g., the Sun, stars, a bulb); secondary sources reflect or scatter light (e.g., the Moon, planets).
- A wavefront is the locus of all points having the same phase at a given instant of time.
- The direction of propagation of light is perpendicular to the wavefront (along the rays).
- A point source produces spherical wavefronts; far from the source, they appear as plane wavefronts.
- A line source produces cylindrical wavefronts; the wave speed equals the speed at which the wavefront moves.
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Law: Huygens' Principle
"Each point on a wavefront acts as a secondary source of light emitting secondary light waves called wavelets in all directions which travel with the speed of light in the medium. The new wavefront can be obtained by taking the envelope of these secondary wavelets travelling in the forward direction and is thus, the envelope of the secondary wavelets in forward direction. The wavelets travelling in the backward direction are in effective".
CBSE: Class 12
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Law: Laws of Reflection
First Law of Reflection:
i = r
The angle of incidence is equal to the angle of reflection.
Second Law of Reflection:
The incident ray, reflected ray, and the normal at the point of incidence lie in the same plane.
CBSE: Class 12
Law: Snell’s Law of Refraction
n1 sin i = n2 sin r
\[\frac{\sin i}{\sin r}=\frac{v_1}{v_2}\]
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Key Points: Total Internal Reflection
- Total internal reflection occurs when light travels from a denser medium to a rarer medium.
- It takes place only when the angle of incidence is greater than the critical angle.
- At angles greater than the critical angle, no refraction occurs.
- The entire light ray is reflected back into the denser medium.
- The intensity of the reflected ray becomes maximum and the phenomenon is used in optical fibres.
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Definition: Critical Angle
The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.
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Formula: Critical Angle
\[
\sin C = \frac{n_2}{n_1}
\]
Where:
For air:
\[
\sin C = \frac{1}{\mu}
\]
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Key Points: Reflection of Light at a Plane Surface
- Reflection at a plane surface can be explained using Huygens’ principle and secondary wavelets.
- The reflected wavefront is formed as the envelope of secondary wavelets produced at the reflecting surface.
- The distance travelled by incident and reflected waves in the same time is equal (AE = BC = vT).
- The size of the image formed by a plane mirror is equal to the size of the object.
- The image formed in a plane mirror shows lateral reversal (right and left are interchanged).
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Key Points: Refraction of Light at a Plane Boundary Between Two Media
- Refraction at a plane boundary can be explained using Huygens’ principle and secondary wavelets.
- When light enters a denser medium, its speed decreases and the wavefronts become closer.
- The refracted image is not laterally inverted, but it appears bent (broken) at the boundary for oblique incidence.
- The wavelength of light changes when it enters a different medium; it decreases in a denser medium.
- The frequency remains unchanged while passing from one medium to another.
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Definition: Unpolarized Light
Light in which the electric field vectors vibrate in all possible directions perpendicular to the direction of propagation.
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Definition: Plane Polarized Light
Light in which the electric field vectors vibrate only in one particular direction perpendicular to the direction of propagation.
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Definition: Polarizer
A material that allows only those light waves to pass whose electric field is along a particular direction (polarizing axis).
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Definition: Plane of Vibration
The plane containing the electric field vectors of plane polarized light is called the plane of vibration.
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Definition: Plane of Polarization
The plane perpendicular to the plane of the vibration and the electric field vector is called plane of polarization.
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Law: Malus’ Law
I2 = I1cos2θ
It gives the intensity of plane polarized light after passing through a second polarizer, where θ is the angle between the axes of the two polarizers.
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Law: Brewster’s Law
Statement
When unpolarized light is incident on a transparent surface at a particular angle (called Brewster’s angle), the reflected light is completely plane polarised.
At this angle, the reflected and refracted rays are perpendicular to each other.
tanθB = \[\frac {n_2}{n_1}\]
where
θB = Brewster’s angle
n1, n2 = refractive indices of the two media
Proof
At Brewster’s angle,
θB + r = 90∘
From Snell’s law:
n1 sin θB = n2 sin r
Since r = 90∘ − θB,
n1 sinθB = n2 cosθB
tan θB = \[\frac {n_2}{n_1}\]
Conclusion
At Brewster’s angle, the reflected light is completely plane polarized and the reflected and refracted rays are mutually perpendicular.
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Definition: Polarization by Scattering
Polarisation by scattering is the phenomenon in which unpolarized light becomes partially or completely plane polarised when it is scattered by small particles such as air molecules or dust particles.
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Definition: Interference
Interference is the phenomenon in which the intensity of light (or any wave) at a point becomes non-uniform due to the superposition of two or more coherent waves, resulting in regions of constructive and destructive interference.
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Key Points: Interference
- Coherent sources emit waves of the same frequency with a constant phase difference.
- In Young’s double slit experiment, two coherent sources are obtained from a single source.
- Condition for constructive interference:
Path difference Δl = nλ
- Condition for destructive interference:
Path difference Δl = (n − \[\frac {1}{2}\])λ
- Position of bright fringe:
yn = \[\frac {nλD}{d}\]
- Fringe width:
W = \[\frac {λD}{d}\]
(Bright and dark fringes are equally spaced.)
- For a clear and steady interference pattern:
Sources must be coherent, monochromatic, of nearly equal amplitude, and slits must be narrow with D ≫ d.
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Defintiion: Diffraction of Light
Diffraction of light is the phenomenon in which light spreads into the geometrical shadow region when it passes around the edges of an obstacle or through a narrow aperture whose size is comparable to its wavelength.
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Definition: Fraunhofer Diffraction
Diffraction observed when the source and screen are at large distances from the diffracting element, so that the incident wavefront is plane.
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Definition: Fresnel Diffraction
Diffraction observed when the source or screen (or both) are at finite distances from the obstacle, and the incident wavefront is spherical or cylindrical.
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Formula: Fraunhofer Diffraction at a Single Slit
\[a\sin\theta=\pm\left(n+\frac{1}{2}\right)\lambda\]
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Formula: Width of the Central Bright Fringe
\[W_{c}=2y_{1d}=2W=2\left(\frac{\lambda D}{a}\right)\]
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Definition: Resolving Power
The ability of an optical instrument to distinguish two closely spaced objects as separate and distinct is called its resolving power.
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Definition: Limit of Resolution
The minimum visual angle between two objects that can be just resolved by an instrument is called the limit of resolution.
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Definition: Resolving Power of Telescope
The resolving power of a telescope is then defined as the reciprocal of the least angular separation between the objects that are just resolved.
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Key Points: Resolving Power
- Resolution depends on diffraction effects caused by the optical instrument's aperture.
- According to Rayleigh’s criterion, two objects are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other.
- For a single slit (linear objects), the limit of resolution:
dθ = \[\frac {λ}{a}\]
- In a microscope, resolving power increases with numerical aperture (N.A. = n sin α) and decreases with wavelength:
R ∝ \[\frac {N.A.}{λ}\]
- For self-luminous point objects (microscope):
a = \[\frac {0.61λ}{N.A.}\]
- For a telescope, angular resolution is:
θ = \[\frac {1.22λ}{D}\]
where D is the aperture diameter.
- Resolving power improves when:
Wavelength is smaller
Aperture diameter is larger
The numerical aperture is higher
CBSE: Class 12
Law: Rayleigh’s Criterion
According to Rayleigh’s criterion, two objects are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other.
