Optics

The One Thing

Optics explains the behaviour of light through two complementary descriptions: ray optics accounts for propagation, reflection, refraction, and image formation, whereas wave optics accounts for interference, diffraction, and polarization. The observed behaviour depends on light’s interaction with media, surfaces, apertures, and other light waves.

Reactions, Processes and Experiments

Key Terms

• Reflection: The return of light into the same medium after striking a surface.
• Laws of Reflection: The incident ray, reflected ray, and normal lie in one plane, and the angle of incidence equals the angle of reflection.
• Refraction: The bending of light as it passes obliquely from one transparent medium to another because its speed changes.
• Refractive Index: A measure of how much a medium slows light, given by $n=c/v$, where $c$ is the speed of light in vacuum and $v$ is its speed in the medium.
• Snell’s Law: For refraction at two media, $n_1\sin i=n_2\sin r$, where $i$ and $r$ are the angles of incidence and refraction.
• Total Internal Reflection: Complete reflection of light inside a denser medium when it travels toward a rarer medium at an angle greater than the critical angle.
• Critical Angle: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90 degrees.
• Spherical Mirror: A reflecting surface forming part of a sphere; it may be concave or convex.
• Mirror Formula: The relation between focal length, object distance, and image distance is $1/f=1/v+1/u$, using the Cartesian sign convention.
• Magnification: The ratio of image size to object size; for a mirror, $m=h_i/h_o=-v/u$.
• Lens: A transparent optical element bounded by two refracting surfaces, usually spherical, that converges or diverges light.
• Lens Formula: The relation for a thin lens is $1/f=1/v-1/u$, using the Cartesian sign convention.
• Power of a Lens: The ability of a lens to converge or diverge light, given by $P=1/f$ when $f$ is measured in metres; its unit is the dioptre.
• Lens Maker’s Formula: For a thin lens in air, $1/f=(n-1)(1/R_1-1/R_2)$, relating focal length to refractive index and radii of curvature.
• Prism: A transparent refracting medium with two plane surfaces inclined at an angle, causing deviation and dispersion of light.
• Dispersion: The splitting of white light into its constituent colours because different wavelengths travel with different speeds in a medium.
• Optical Fibre: A fibre that transmits light through repeated total internal reflection; it is used in communication and medical imaging.
• Simple Microscope: A convex lens used as a magnifying glass to produce an enlarged virtual image.
• Compound Microscope: An instrument using an objective lens and an eyepiece to obtain high angular magnification of small objects.
• Astronomical Telescope: An instrument that uses an objective and an eyepiece to view distant objects with increased angular magnification.
• Resolving Power: The ability of an optical instrument to distinguish two closely spaced objects as separate.
• Huygens’ Principle: Every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is their common envelope.
• Wavefront: A surface joining points of a wave that are in the same phase.
• Coherent Sources: Sources that emit waves of the same frequency and maintain a constant phase difference.
• Interference: The redistribution of intensity caused by the superposition of coherent light waves.
• Constructive Interference: Reinforcement of waves producing maximum intensity when path difference is $n\lambda$.
• Destructive Interference: Cancellation of waves producing minimum intensity when path difference is $(2n+1)\lambda /2$.
• Young’s Double-Slit Experiment: An experiment demonstrating interference and providing the fringe-width relation $\beta =\lambda D/d$.
• Diffraction: The bending and spreading of waves around obstacles or through narrow apertures.
• Polarization: The restriction of light vibrations to a particular direction perpendicular to the direction of propagation.
• Brewster’s Law: At the polarizing angle, the refractive index satisfies $n=\tan i_p$.
• Malus’ Law: The transmitted intensity through an analyser is $I=I_0{\cos }^2\theta$, where $\theta$ is the angle between the transmission axes.
• Real Image: An image formed by actual convergence of rays and capable of being obtained on a screen.
• Virtual Image: An image formed by apparent convergence of rays and incapable of being obtained on a screen.
• Geometrical Optics: The approximation in which light is treated as travelling along straight rays when apertures and obstacles are much larger than the wavelength.
• Numerical Aperture: A measure of the light-gathering ability of an optical fibre, given in air by $\mathrm{NA}=\sqrt{(n_1^2-n_2^2)}$.
• Electromagnetic Spectrum: The range of electromagnetic radiation arranged according to wavelength or frequency; visible light occupies only a small part of it.

Easily Confused

• Reflection and refraction: Reflection returns light into the same medium, whereas refraction bends light as it enters another transparent medium.
• Real and virtual images: A real image is formed by actual ray convergence and can be screened; a virtual image is formed by apparent convergence and cannot be screened.
• Constructive and destructive interference: Constructive interference gives maximum intensity when the path difference is $n\lambda$, whereas destructive interference gives minimum intensity when it is $(2n+1)\lambda /2$.
• Interference and diffraction: Interference concerns the superposition of coherent waves, whereas diffraction is the bending and spreading around obstacles or through apertures.
• Magnification and resolving power: Magnification increases apparent size, whereas resolving power determines whether closely spaced objects can be distinguished.
• Critical angle and total internal reflection: The critical angle gives 90 degrees refraction in the rarer medium; total internal reflection occurs when the incidence angle exceeds it.
• Ray optics and wave optics: Ray optics describes propagation and image formation, whereas wave optics explains interference, diffraction, and polarization.
• Simple and compound microscopes: A simple microscope uses one convex lens, whereas a compound microscope uses an objective lens and an eyepiece.
• Microscope and telescope: A microscope magnifies small nearby objects, whereas an astronomical telescope magnifies the angular size of distant objects.
• Polarization and dispersion: Polarization restricts the direction of light vibrations, whereas dispersion separates light according to wavelength.
• Mirror and lens formulae: The mirror formula is $1/f=1/v+1/u$, whereas the lens formula is $1/f=1/v-1/u$.
• Mirror and lens magnification: For a mirror, $m=h_i/h_o=-v/u$; for a lens, $m=h_i/h_o=v/u$.
• Transverse and longitudinal waves: Light can be polarized because it is transverse; sound waves in air cannot be polarized because they are longitudinal.

What Gets Asked

• Numerical problems using mirror and lens formulae: Apply the Cartesian sign convention consistently, measuring mirror distances from the pole and lens distances from the optical centre, with the direction of incident light usually taken as positive.
• Problems involving total internal reflection: State both conditions: light must travel from an optically denser medium to a rarer medium, and the angle of incidence must exceed the critical angle.
• Prism calculations: At minimum deviation, use $n=\sin [(A+{\delta }_m)/2]/\sin (A/2)$; do not confuse prism angle $A$ with minimum deviation ${\delta }_m$.
• Optical-instrument calculations: Use the stated formula for simple-microscope magnifying power, distinguish final image at infinity from final image at the least distance of distinct vision, and remember that compound-microscope magnifying power depends on objective and eyepiece focal lengths and tube length.
• Young’s double-slit questions: Use $\beta =\lambda D/d$, and distinguish bright fringes at path difference $n\lambda$ from dark fringes at path difference $(2n+1)\lambda /2$.
• Diffraction and resolution questions: For single-slit minima use $a\sin \theta =n\lambda$; remember that the central maximum is approximately twice as wide as each secondary maximum, and that resolution improves with shorter wavelength, larger numerical aperture, or larger telescope aperture as appropriate.