Chapter 9 · Introduction

Chapter 9 — Ray Optics and Optical Instruments

Light travels in straight lines until it meets a mirror, a surface between two media or a lens. Four simple rules — the laws of reflection and refraction, applied with one sign convention — explain mirrors, optical fibres, lenses, prisms, microscopes and telescopes.

A dentist's mouth mirror, the wing mirror of a car that warns "objects are closer than they appear", the lens of your phone camera, the spectacles on a classmate's nose and the hair-thin glass fibres that carry this page to your screen at the speed of light all do the same few things to light: they reflect it or bend it. In the 1990s an optician's error of about one-fiftieth of a millimetre in the main mirror of the Hubble Space Telescope blurred every image it took — and the repair, a set of correcting mirrors fitted by astronauts in orbit, was designed with exactly the formulas of this chapter.

In Class 10 Physics (Light — Reflection and Refraction, and The Human Eye) you met the laws of reflection and refraction and drew ray diagrams for mirrors and lenses. Here we make that picture quantitative. We fix one sign convention and derive the mirror equation; we explain refraction with the refractive index and find when light cannot leave a dense medium at all — total internal reflection, the principle of the optical fibre. Applying Snell's law at a curved surface gives the lens maker's formula and the thin-lens formula, and two simple ideas — power in dioptres and the prism's angle of minimum deviation — lead to the design of the microscope and the telescope. In Chapter 8 you learned that light is an electromagnetic wave; in this chapter we only need its rays, the straight lines along which its energy travels.

Mirrors & sign convention→Refraction, $n$→Total internal reflection→Curved surfaces & lenses→Power, combinations→Prism, $\delta_m$→Microscopes & telescopes

🎯 By the end of this chapter you can…

use the Cartesian sign convention, derive $f=R/2$ and the mirror equation, and find the position, size and nature of the image formed by a concave or convex mirror;
state Snell's law with the refractive index, explain apparent depth, and find the critical angle and the conditions for total internal reflection in prisms and optical fibres;
derive the formula for refraction at a spherical surface, the lens maker's formula and the thin-lens formula, and use power in dioptres for lenses in contact;
derive the prism formula, find the refractive index from the angle of minimum deviation, and use $\delta=(n-1)A$ for a thin prism;
explain the simple and compound microscope and the refracting and reflecting telescope, and calculate their magnifying powers;
solve board, JEE Main, JEE Advanced and NEET problems on all of the above.

Light leaves the lamp $A$ in air and must reach the point $B$ under water ($n=1.33$, where light is $1.33$ times slower). Which crossing point $P$ on the surface does it use? Drag $P$ (or press Play to sweep it): the graph on the right shows the travel time for every choice. The real ray — the green line — crosses where the time is least, and there $\sin i/\sin r$ equals the refractive index. That is Snell's law, which we use from Section 9.2 onwards. (A teaser: the least-time idea itself is not needed for the examinations.)

Lower medium:

crossing point $x_P$—

travel time—

$\sin i/\sin r$—

least time (green ray)—

Sections in this chapter

9.1

Reflection of Light by Spherical Mirrors

The Cartesian sign convention, focal length and radius of curvature, the mirror equation, magnification and ray diagrams.

$\dfrac1v+\dfrac1u=\dfrac1f$, $\ f=\dfrac R2$

Open section →9.2

Refraction and Total Internal Reflection

Snell's law and the refractive index, apparent depth, the critical angle, total internal reflection in prisms, diamonds and optical fibres.

$n_1\sin i=n_2\sin r$, $\ \sin C=\dfrac1n$

Open section →9.3

Refraction at Spherical Surfaces and by Lenses

A single curved surface, the lens maker's formula, the thin-lens formula, power in dioptres and lenses in contact.

$\dfrac1v-\dfrac1u=\dfrac1f$, $\ P=\dfrac1f$

Open section →9.4

Refraction through a Prism and Optical Instruments

Deviation and the angle of minimum deviation, thin prisms, the eye, simple and compound microscopes, refracting and reflecting telescopes.

$n=\dfrac{\sin\frac{A+\delta_m}{2}}{\sin\frac A2}$, $\ m=\dfrac{f_o}{f_e}$

Open section →

✅ Before you start

From Class 10 Physics (Light — Reflection and Refraction; The Human Eye and the Colourful World) you need the laws of reflection, the names of the parts of mirrors and lenses, the standard ray diagrams, the idea of a real and a virtual image, and the eye's near point and far point. Dispersion of white light into a spectrum, the rainbow and the scattering of light (the blue sky, the red sunset) were explained there and are not repeated in this course. From mathematics you need trigonometry — $\sin$, $\cos$, $\tan$ and the small-angle approximations $\sin\theta\approx\tan\theta\approx\theta$ (in radians) — and the algebra of fractions. Chapter 8 (light as an electromagnetic wave travelling at $c=3.0\times10^8$ m/s in vacuum) is useful background but not required. No calculus is used in this chapter.

← 8.2 Electromagnetic Waves and the Electromagnetic Spectrum 9.1 Reflection of Light by Spherical Mirrors →