## 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 i_{c}for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > i_{c},**total internal reflection**Multiple internal reflections in diamond (i_{c }≅ 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

f is negative for concave mirror; f is positive for a convex mirror.

**object and image distances**respectively,**of the mirror, f is (approximately) half the**

f is the focal lengthf is the focal length

**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 n

where D

_{2}placed in a medium of refractive index n_{1},where D

_{m}is the angle of minimum deviation.
For

R

f is positive for a converging lens,

f is negative for a diverging lens.

The

The SI unit for power of a lens is dioptre (D): 1D = 1m

If several thin lenses of focal length f

The

**refraction through a spherical interface**(from medium 1 to 2 of refractive index n_{1}and n_{2}, respectively)**Thin lens formula:****Lens maker’s formula**:R

_{1}and R_{2}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 f

_{1}, f_{2}, f_{3}… are in contact, the**effective focal length**of their combination, is given by,The

**total power**of a combination of several lenses is P = P_{1}+ P_{2}+ 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,

**is the focal length of the convex lens.**

f

f

If the image is at infinity,

**m = D/f**

For a

**compound microscope**, the magnifying power is given by,>

**m = m**

_{e}× m_{0}where,

**m**, is the magnification due to the eyepiece

_{e}= 1 + (D/f_{e})**m**is the magnification produced by the objective.

_{o}Approximately, Where

**f**and

_{o}**f**are the focal lengths of the objective and eyepiece, respectively,

_{e}**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

**f**and

_{0}**f**are the focal lengths of the objective and eyepiece, respectively.

_{e}