Ray Optics and Optical Instruments

Comprehensive vocabulary flashcards covering reflection, spherical mirrors, refraction, total internal reflection, lenses, prisms, and optical instruments from Chapter 9 of Ray Optics and Optical Instruments.

Light

Electromagnetic radiation detected by the human retina belonging to the visible spectrum, with a wavelength ranging from about $400\,\text{nm}$ to $750\,\text{nm}$.

Ray of light

The straight-line path along which a light wave travels from one point to another.

Beam of light

A bundle of rays of light.

Pole

The geometric centre of a spherical mirror.

Optical centre

The geometric centre of a spherical lens.

Principal axis (spherical mirror)

The straight line joining the pole and the centre of curvature of a spherical mirror.

Cartesian sign convention

The convention where all distances are measured from the pole of the mirror or optical centre of the lens along the principal axis; distances in the direction of incident light are positive, opposite are negative, heights upwards are positive, and heights downwards are negative.

Paraxial rays

Rays of light that are incident at points close to the pole of the mirror and make small angles with the principal axis.

Principal focus (spherical mirror)

The point $F$ on the principal axis where rays incident parallel to the principal axis converge (in a concave mirror) or appear to diverge from (in a convex mirror) after reflection.

Focal plane

The plane perpendicular to the principal axis passing through the principal focus, where parallel paraxial rays incident at an angle to the axis converge or appear to diverge.

Focal length ($f$)

The distance between the principal focus ($F$) and the pole ($P$) of a mirror or optical centre of a lens; for spherical mirrors, $f = \frac{R}{2}$.

Real image

An image formed when light rays emanating from an object point actually converge and intersect at another point after reflection or refraction.

Virtual image

An image formed when light rays emanating from a point do not actually meet after reflection or refraction, but appear to diverge from that point when produced backwards.

Mirror equation

The mathematical relation connecting object distance ($u$), image distance ($v$), and focal length ($f$) of a spherical mirror: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.

Linear magnification (spherical mirror)

The ratio of the height of the image ($h'$) to the height of the object ($h$), expressed as $m = \frac{h'}{h} = -\frac{v}{u}$.

Refraction of light

The change in the direction of propagation of an obliquely incident ray of light ($0^\circ < i < 90^\circ$) as it enters across the interface from one transparent medium into another.

Snell's law of refraction

The law stating that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media: $\frac{\sin(i)}{\sin(r)} = n_{21}$.

Refractive index ($n_{21}$)

A characteristic constant for a pair of media equal to the ratio of the sine of the angle of incidence in medium 1 to the sine of the angle of refraction in medium 2, representing the ratio of optical speeds in the media.

Optically denser medium

A medium in which the refractive index relative to another medium is greater than one ($n_{21} > 1$), causing the refracted ray to bend towards the normal ($r < i$).

Optically rarer medium

A medium in which the relative refractive index is less than one ($n_{21} < 1$), causing the refracted ray to bend away from the normal ($r > i$).

Lateral shift

The perpendicular displacement between the incident ray and the emergent ray after refraction through a parallel-sided transparent slab.

Apparent depth

The perceived depth ($h_1$) of an object submerged in an optically denser medium when viewed from near normal, given by real depth ($h_2$) divided by the refractive index of the medium ($h_1 = \frac{h_2}{n}$).

Total internal reflection

The complete reflection of a light ray back into an optically denser medium when it strikes the interface with an optically rarer medium at an angle of incidence greater than the critical angle.

Critical angle ($i_c$)

The angle of incidence in an optically denser medium for which the angle of refraction in the rarer medium is $90^\circ$, given by $\sin(i_c) = n_{21} = \frac{1}{n_{12}}$.

Optical fibre

A thin, flexible strand fabricated from high-quality composite glass or quartz consisting of a central core of higher refractive index and an outer cladding of lower refractive index, guiding light by repeated total internal reflection.

Thin lens

A transparent optical medium bounded by two surfaces, at least one of which is spherical, with a thickness that is negligible compared to the radii of curvature.

Lens maker's formula

The formula relating the focal length of a lens to the refractive indices of the media and the radii of curvature of its two surfaces: $\frac{1}{f} = \left(\frac{n_2}{n_1} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$.

Thin lens formula

The equation relating object distance ($u$), image distance ($v$), and focal length ($f$) of a thin lens: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.

Power of a lens

A quantitative measure of the convergence or divergence introduced by a lens, defined as the tangent of the angle by which it deviates a beam parallel to the axis at unit distance from the optical centre: $P = \frac{1}{f}$.

Dioptre ($\text{D}$)

The SI unit of the power of a lens, equivalent to $1\,\text{m}^{-1}$, corresponding to the power of a lens with a focal length of $1\,\text{m}$.

Angle of deviation ($\delta$)

The angle between the emergent ray and the original direction of the incident ray passing through a prism, given by $\delta = i + e - A$.

Angle of minimum deviation ($D_m$)

The minimum value of deviation produced by a prism where the refracted ray inside the prism travels parallel to its base, satisfying $i = e$ and $r = \frac{A}{2}$.

Near point ($D$)

The closest comfortable viewing distance for distinct vision with the human eye without strain, typically taken as $D \approx 25\,\text{cm}$.

Simple microscope

An optical magnifying instrument consisting of a single converging lens of short focal length used to view objects erect, magnified, and virtual.

Compound microscope

An optical device consisting of two converging lenses—an objective and an eyepiece—used to achieve high total magnification of small objects.

Objective (microscope)

The converging lens in a compound microscope placed nearest the object, having a short focal length and small aperture, which forms a real, inverted, magnified image.

Eyepiece

The lens of a microscope or telescope positioned nearest the observer's eye, which acts as a simple magnifier to enlarge the intermediate image formed by the objective.

Tube length ($L$)

The distance between the second focal point of the objective and the first focal point of the eyepiece in a compound microscope.

Telescope

An optical instrument designed to provide angular magnification of distant objects, featuring an objective of large focal length and aperture and an eyepiece of small focal length.

Reflecting telescope

A telescope that employs a concave mirror instead of a lens as its objective to eliminate chromatic aberration and minimize mechanical support issues.

Cassegrain telescope

A type of reflecting telescope that uses a large concave primary mirror with a central hole and a secondary convex mirror that directs light back through the hole to the eyepiece.

Dispersion

The phenomenon of the splitting of light into its constituent colours when passing through a refracting medium.