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

The radius of the sphere of which the reflecting surface of a spherical mirror forms a part is called the radius of curvature of the mirror. It is represented by the letter R.

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The radius of the sphere of which the mirror forms a part, is called the 'radius of curvature' of the mirror.

A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.

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A convex mirror is one whose reflecting surface is away from the centre of the sphere of which the mirror is a part.

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The reflecting surface is on the outer side of the sphere (diverging mirror).

A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror.

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A concave mirror is one whose reflecting surface is towards the centre of the sphere of which the mirror is a part.

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The reflecting surface is on the inner side of the sphere (converging mirror).

Mirrors whose reflecting surfaces are spherical are called spherical mirrors.

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A spherical mirror is a part of a hollow sphere, whose one side is silvered and coated with red oxide and the other side is the reflecting surface.

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A spherical mirror is a piece cut out of a spherical surface, which can be concave or convex.

Aperture is the distance between the extreme points on the periphery of the mirror.

 Centre of curvature is the centre of the imaginary sphere to which the mirror belongs.

Principal focus of a spherical mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror, converge to or appear to diverge from.

“A mirror which is made from a part of a hollow sphere is called Spherical Mirror.

“A mirror made by silvering the inner surface such that reflection takes place from the bulging surface” is called Convex Mirror.
The Centre of curvature is towards the silvered surface.

“A mirror made by silvering the outer or the bulging surface such that the reflection takes place from the concave surface.” Centre of curvature is towards the reflecting surface.

Pole “is the mid-point of the mirror”.

The centre of a hollow sphere of which the mirror forms a part is called the centre of curvature.

An imaginary line passing through the pole and the centre of curvature of a spherical mirror is called principal axis.

It is a point on the principal axis, where a beam of light, parallel to the principal axis, after reflection actually meet.

The linear distance between the pole and the center of curvature is called the radius of curvature.

The linear distance between the pole and the principal focus is called focal length.

The focus of a concave mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror converge to that point.

Normal to the surface of a mirror at any point is the straight line at the right angle to the tangent drawn at that point.

The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C.

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The centre of the sphere of which the mirror forms a part, is called the ‘centre of curvature' of the mirror.

The distance between the pole and the principal focus is called the focal length (f) of a spherical mirror.

Pole is the centre of the reflecting surface, in this case, a spherical mirror.

The centre of the reflecting surface of a spherical mirror is a point called the pole. The pole is usually represented by the letter P.

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The central point of the reflecting surface of the mirror is called the 'pole' of the mirror.

A straight line passing through the pole and the centre of curvature of a spherical mirror. This line is called the principal axis.

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The straight line joining the pole and the centre of curvature of the mirror and extended on both sides is called the 'principal axis' of the mirror.

Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.

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When light passes from one transparent medium to another, its speed and direction change. This is called refraction.

Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

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Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

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The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.

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When a ray of light impinges on a polished, smooth, shiny surface, the rebounding of light within the same medium is called reflection of light.

A prism is a transparent medium bounded by five plane surfaces with a triangular cross-section.

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

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

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.

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.

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).

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

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

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

When I₁ = I₂ = I₀:

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

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

Defined as dipole moment per unit volume:

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

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.

• 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.