Ray Optics and Optical Instruments
Reflection, refraction, lenses, mirrors, and the instruments that extend human vision
Table of Contents
9.1 Introduction
Nature has endowed the human eye (retina) with the sensitivity to detect electromagnetic waves within a small range of the electromagnetic spectrum. Electromagnetic radiation belonging to this region of the spectrum (wavelength of about 400 nm to 750 nm) is called light. It is mainly through light and the sense of vision that we know and interpret the world around us.
9.2 Reflection at Spherical Mirrors
Spherical mirrors (concave and convex) follow the mirror formula:
- Concave mirror: Converging. Real, inverted image (except when object is within focal length)
- Convex mirror: Diverging. Always produces virtual, erect, diminished image
- Magnification: m = βv/u = height of image/height of object
9.3 Refraction
Refraction is the bending of light as it passes from one medium to another with a different refractive index:
9.4 Total Internal Reflection
Total internal reflection (TIR) occurs when light travels from a denser medium to a rarer medium at an angle greater than the critical angle:
Optical fibres (communication), diamonds (brilliance), mirages (desert illusion), prism binoculars, periscopes with totally reflecting prisms.
9.5 Refraction at Spherical Surfaces
For refraction at a single spherical surface:
9.6 Thin Lenses
The thin lens formula relates object distance, image distance, and focal length:
Convex (Converging) Lens
Converges parallel rays to focal point. Real or virtual image depending on object position. f > 0.
Concave (Diverging) Lens
Diverges parallel rays. Always produces virtual, erect, diminished image. f < 0.
9.7 Prism and Dispersion
A prism deviates light by an angle that depends on the refractive index and the prism angle:
9.8 Optical Instruments
Microscope
m = mβ Γ m_e = (D/f_o)(L/f_e). Simple microscope: converging lens held near object. Compound: two lenses for higher magnification.
Telescope
m = βf_o/f_e. Large objective collects light from distant objects. Small eyepiece acts as magnifier. Resolving power β 1/d.
The minimum angular separation between two point objects that can be distinguished: ΞΈ_min = 1.22Ξ»/d (Rayleigh criterion). Larger aperture d gives better resolving power.