## RAY OPTICS AND OPTICAL INSTRUMENTS

 Reflection of light by spherical mirrors Sign convention (Cartesian rule) Focal length of spherical mirrors Focal length of spherical mirrors Derivation of the relation f = R/2 in the case of a concave mirror -Mirror equation: Derivation of mirror equation in the case of concave mirror producing a real image Definition and expression for linear magnification. Refraction of light Explanation of phenomenon Laws of refraction Consequences Total internal reflection Explanation of phenomenon Mention of conditions Definition of critical angle Mention the relation between n and ic Mention of its applications (mirage, total reflecting prisms and optical fibers) Refraction at spherical surfaces Derivation of the relation between u, v, n and R. Refraction by a Lens Derivation of lens-maker’s formula Mention of thin lens formula Definition and expression for linear magnification Power of a lens and mention of expression for it Combination of thin lenses in contact Derivation of equivalent focal length of two thin lenses in contact Refraction of light through a prism Derivation of refractive index of the material of the prism Dispersion by prism Scattering of light Rayleigh’s scattering law Blue colour of the sky and reddish appearance of the sun at sunrise and sunset Optical instruments: Eye Accommodation and least distance of distinct vision Correction of eye defects (myopia and hypermetropia) using lenses Simple microscope Ray diagram for image formation Mention of expression for the magnifying power Compound microscope Ray diagram for image formation Mention of expressions for the magnifying power when the final image is at (a) least distance of distinct vision and (b) infinity Telescope Ray diagram for image formation Mention of expression for the magnifying power and length of the telescope (L = fo + fe) – Schematic ray diagram of reflecting telescope Numerical Problems

## Snell’s law :

Reflection is governed by the equation ∠i = ∠r′ and refraction by the Snell’s law, sin i/sin r = n, where the incident ray, reflected ray, refracted ray and normal lie in the same plane. Angles of incidence, reflection and refraction are i, r ′ and r, respectively.
The critical angle of incidence ic for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > ic, total internal reflection Multiple internal reflections in diamond (ic ≅ 24.4°), totally reflecting prisms and mirage, are some examples of total internal reflection.

## Optical fibres:

Optical fibres consist of glass fibres coated with a thin layer of material of lower refractive index. Light incident at an angle at one end comes out at the other, after multiple internal reflections, even if the fibre is bent. These optical fibers work on the principle of total internal reflection.

## Cartesian sign convention:

• Distances measured in the same direction as the incident light are positive.
• Those measured in the opposite direction are negative.
• All distances are measured from the pole/optic centre of the mirror/lens on the principal axis.
• The heights measured upwards above x-axis and normal to the principal axis of the mirror/ lens are taken as positive. The heights measured downwards are taken as negative.

## Mirror equation: where u and v are object and image distances respectively,
f is the focal length
of the mirror, f is (approximately) half the radius of curvature R.
f is negative for concave mirror; f is positive for a convex mirror.
For a prism of the angle A, of refractive index n2 placed in a medium of refractive index n1, where Dm is the angle of minimum deviation.
For refraction through a spherical interface (from medium 1 to 2 of refractive index n1 and n2, respectively) Thin lens formula: Lens maker’s formula: R1 and R2 are the radii of curvature of the lens surfaces.
f is positive for a converging lens,
f is negative for a diverging lens.
The power of a lens P = 1/f.
The SI unit for power of a lens is dioptre (D): 1D = 1m–1.
If several thin lenses of focal length f1, f2, f3… are in contact, the effective focal length of their combination, is given by, The total power of a combination of several lenses is P = P1 + P2 + P3 + …

## Dispersion:

Dispersion is the splitting of light into its constituent colours.

## Magnifying power:

Magnifying power m of a simple microscope is given by, m = 1 + (D/f )
where D = 25 cm is the least distance of distinct vision,
f
is the focal length of the convex lens.
If the image is at infinity, m = D/f
For a compound microscope, the magnifying power is given by,>
m = me × m0
where, me = 1 + (D/fe), is the magnification due to the eyepiece
mo is the magnification produced by the objective.
Approximately, Where fo and fe are the focal lengths of the objective and eyepiece, respectively,
L is the distance between their focal points.

## Magnifying power (m) of a telescope:

Magnifying power m of a telescope is the ratio of the angle β subtended at the eye by the image to the angle α subtended at the eye by the object. where f0 and fe are the focal lengths of the objective and eyepiece, respectively.