Revision: Wave Optics Physics HSC Science Class 12 Tamil Nadu Board of Secondary Education

The phenomenon of redistribution of energy on account of superposition of light waves from two coherent sources is called interference of light.

The phenomenon that occurs when two waves meet while travelling along the same medium is called wave interference.

The points of maximum intensity in the regions of superposition of waves are said to be in constructive interference.

The points of minimum intensity in the regions of superposition of waves are said to be in destructive interference.

The bending of light near the edge of an obstacle or slit and spreading into the region of geometrical shadow is called diffraction of light.

The type of diffraction that occurs when the source or screen is at a finite distance from the diffracting object and fringes are not sharp and well-defined is called Fresnel diffraction.

The type of diffraction that occurs when the source and the observation screen are far away (effectively at infinite distance) from the diffracting object and fringes are not sharp and well-defined is called Fraunhofer diffraction.

Alignment of dipole moments (permanent or induced) in the direction of an applied electric field is called polarisation.

Angular magnification or magnifying power of an optical instrument is defined as the ratio of the visual angle made by the image formed by that optical instrument (β) to the visual angle subtended by the object when kept at the least distance of distinct vision (α).

An optical instrument that uses a single convex lens to magnify small objects is called a simple microscope.

An optical instrument that uses objective and eye piece lenses to magnify tiny objects in detail is called a compound microscope.

The resolving power of an astronomical telescope is defined as the reciprocal of the smallest angular separation between two point objects whose images can just be resolved by the telescope.

R.P = `(1.22 lambda)/D`

Resolving power is the ability of the telescope to distinguish clearly between two points whose angular separation is less than the smallest angle that the observer’s eye can resolve.

An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.

I = I₁ ​+ I₂​ + 2\[\sqrt {I_1​I_2}\] ​​⋅ cos ϕ

When I₁ = I₂ = I₀:

I = \[2I_0(1+\cos\phi)=4I_0\cos^2\left(\frac{\phi}{2}\right)\]

\[\frac{I_{\max}}{I_{\min}}=\left(\frac{a_1+a_2}{a_1-a_2}\right)^2=\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2\]

When two waves of amplitudes a₁ and a_2​ interfere at a point where phase difference is ϕ, the resultant amplitude is:

\[A^2=a_1^2+a_2^2+2a_1a_2\cos\phi\]

Defined as dipole moment per unit volume:

\[P=\frac{\text{dipole moment}}{\mathrm{volume}}=np\]

1. M_Max = 1 + \[\frac {D}{f}\]
2. M_Min = \[\frac {D}{f}\]

M = m_o × M_e

1. \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
2. M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]

The law of refraction is called Snell’s law.

Snell’s law states that,

1. The incident ray, refracted ray and normal to the refracting surface are all coplanar (i.e., lie in the same plane).
2. The ratio of the angle of incidence i in the first medium to the angle of reflection r in the second medium is equal to the ratio of the refractive index of the second medium n₂ to that of the refractive index of the first medium n₁.
   `(sin "i")/(sin "r") = "n"_2/"n"_1`

Thomas Young first demonstrated the phenomenon of interference of light with the help of a slit, using a monochromatic source and two slits S₁ and S₂​, producing alternating bright fringes (constructive interference) and dark fringes (destructive interference) on a screen.

• Every point on a wavefront acts as a secondary source (point source) that emits new spherical wavelets in all directions with the same speed as the original wave.
• The new (forward) wavefront at any later time is the common tangential envelope (tangent surface) to all these secondary wavelets.
• The wavefront in a medium is always perpendicular to the direction of wave propagation.
• Secondary wavelets travel only in the forward direction — backward wavelets are ignored (zero amplitude in backward direction).

Memory: Every point → new source → envelope = new wavefront.

• Diffraction = bending and spreading of light waves around obstacles or through narrow openings, producing interference patterns.
• It is due to interference of secondary wavelets from the exposed portion of the wavefront from the slit.
• Key difference from interference: in diffraction, bright fringes have same intensity but bands are of decreasing intensity.

Single Slit Diffraction:

Let a = width of slit, θ = angle of diffraction.

Condition for Minimum (Dark) Intensity:

Condition for Maximum (Secondary Bright) Intensity:

\[a\sin\theta=(2n+1)\frac{\lambda}{2},\quad n=1,2,3...\]

Width of Central Maximum:

For first minima: \[a\cdot\frac{y}{D}=\lambda\Rightarrow y=\frac{\lambda D}{a}\]

\[W=2y=\frac{2\lambda D}{a}\]

Angular width of central maximum:

Linear width of n-th secondary maximum:

• An optical instrument uses the principles of optics to enhance, modify, or analyse light for specific purposes.
• They manipulate light through reflection, refraction, diffraction, or interference.
• Common instruments: simple microscope, compound microscope, telescope.

Astronomical (Refracting) Telescope:

• Used to view distant objects.
• Objective lens (large focal length) forms image A'B' at its focus → acts as object for eyepiece.
• Eyepiece forms the final virtual, magnified image A''B''.

Magnifying Power: \[MP=\frac{\text{Visual angle with instrument}(\beta)}{\text{Visual angle for unaided eye}(\alpha)}\]

Resolving Power of Telescope:

• Ability to produce distinct images of two closely spaced objects.
• Angular separation between two resolvable objects: \[\sin\theta=1.22\frac{\lambda}{d}\]​ (Rayleigh's criterion), where d = aperture.
• Resolving power is inverse of angular separation.
• Larger aperture → better resolving power.

Types of Telescope:

• Refracting telescope: Uses two convex lenses; large objective + small eyepiece.
• Reflecting telescope: Uses concave mirror to reflect light internally; secondary mirror directs to eyepiece.
• Keplerian telescope: Converging lens as eyepiece → inverted image.
• Galilean telescope: Diverging lens as eyepiece → erect image.
• Magnification of Refracting Telescope: \[M=\frac{f_{o}}{f_{e}}\]