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

If a point source emits waves uniformly in all directions, the locus of points which have the same amplitude and vibrate in the same phase is a sphere. This is known as a spherical wave.

At a large distance from the source, a small portion of the spherical wave can be considered as a plane. This is known as a plane wave.

A wavefront is a surface of constant phase.

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

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

Diffraction is the phenomenon of bending of light (or any wave) around the corners or edges of an obstacle or aperture, causing it to spread into the geometrical shadow region and produce alternate dark and bright regions.

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).

For a normal, unaided human eye, D = 25 cm. If an object is brought closer than this, we cannot see it clearly. The minimum distance from the eye at which an object can be seen clearly is called the least distance of distinct vision.

OR

Due to the limitation of focusing the eye lens, it is not possible to take an object closer than a certain distance. This distance is called the least distance of distinct vision.

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.

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

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.

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.