Lecture 1 and 2 propagation and velocity of light

Q: What is optics?

A: The science of light.

Q: Compare geometrical optics and physical optics.

Geometrical Optics (Ray Optics)

Light treated as rays

Reflection

Refraction

Mirrors

Prisms

Lenses

Physical Optics (Wave Optics)

Light treated as waves

Interference

Diffraction

Polarisation

Q: Compare a point source and an extended source.

Point source

Very small source of light

Extended source

Consists of many point sources or has appreciable size

Q: What is the first law of geometrical optics?

Light propagates in straight lines through a homogeneous transparent medium.

Rectilinear propagation of light.

Q: What does the wave theory of light state?

Light is part of the electromagnetic spectrum and behaves as a wave.

Q: Who proposed the particle and wave theories of light?

Newton → light as particles

Huygens → light as waves

Q: What is Huygens' Principle?

Every point on a wavefront acts as a source of secondary wavelets, which combine to form a new wavefront.

Q: Define isotropic and homogeneous media.

Isotropic

Same properties in all directions

Homogeneous

Same properties throughout the medium

Q: What is a wavefront?

An imaginary surface joining points that are in the same phase.

Q: What are wavelength, frequency and amplitude?

Wavelength (λ)

Distance between two successive points in the same phase.

Frequency (ν)

Number of complete waves produced per second.

Amplitude (A)

Maximum height/depth of a wave.

Q: What is the relationship between velocity, frequency and wavelength?

Velocity = Frequency × Wavelength

Q: What is the speed of light in a vacuum?

3×108 m s−1

Same for all colours of light.

Q: What is a ray of light?

An imaginary straight-line path showing the direction in which light travels through a homogeneous medium.

Q: What is a pencil of rays?

A group of light rays.

Types:

Divergent

Convergent

Parallel

The central ray is called the chief ray.

Q: What is vergence?

Vergence is the reciprocal of the distance from a point to the source or focus.

​Unit = Dioptre (D)

Q: Explain the sign convention for vergence.

Positive (+)

Distance measured in the same direction as the light travels.

Negative (-)

Distance measured opposite to the direction of light travel.

Memory trick: Move with light = + Move against light = -

Q: What is a dioptre?

The unit of vergence.

1 D = vergence of rays whose source or focus is 1 metre away.

Q: What do the symbols l, l′, L and L′ represent?

Object side

l = object distance

L = object vergence

Image side

l′ = image distance

L′ = image vergence

Q: Explain propagation and velocity of light.

Optics is the science of light.

Geometrical optics treats light as rays and explains reflection, refraction, mirrors, prisms and lenses.

Physical optics treats light as waves and explains interference, diffraction and polarisation.

The first law of geometrical optics states that light travels in straight lines through a homogeneous transparent medium.

Newton proposed the particle theory; Huygens proposed the wave theory.

Huygens' Principle states that every point on a wavefront acts as a source of secondary wavelets.

A wavefront joins points in the same phase.

Optical media may be isotropic (same properties in all directions) and homogeneous (same properties throughout).

Wavelength is the distance between successive points in phase.

Frequency is the number of waves per second.

Amplitude is wave height.

The relationship is:

v=νλv=\nu\lambdav=νλ

The speed of light in vacuum is 3×108 m s−13\times10^8\ \text{m s}^{-1}3×108 m s−1.

A ray is an imaginary straight-line path of light.

A pencil of rays may be divergent, convergent or parallel.

Vergence is the reciprocal of distance from a source or focus.

The unit of vergence is the dioptre.

Distances measured with the direction of light are positive; against the direction of light are negative.

Q: How do you calculate vergence from distance?

L=l/1​

Q: What is the relationship between wavefront curvature and radius of curvature?

Curvature (R) is the reciprocal of the radius of curvature (r).

R=r/1​

Q: Where is the centre of curvature of a diverging wavefront?

For spherical wavefronts diverging from a point source, the centre of curvature coincides with the source.

Q: Compare vergence and curvature.

Both are calculated as reciprocals:

L=1/l

R=1/r

Vergence describes the convergence/divergence of light.

Curvature describes the shape of the wavefront.

Q: What happens to vergence and curvature as distance/radius increases?

As distance increases, vergence decreases.

As radius of curvature increases, curvature decreases.

Large distance = low vergence

Large radius = low curvature