Wave Optics: Doppler Effect

Change in the observed frequency of light when the source or observer is moving relative to each other, significant even at high speeds.

Δν/ν = v_radial/c, where Δν is the change in observed frequency, ν is the original frequency, v_radial is the radial velocity, and c is the speed of light.

Component of velocity along the line connecting the observer and source.

Equals the frequency of incident light.

Decreases when light travels from a rarer to a denser medium.

Determined by the number of photons crossing a unit area per unit time.

Frequency does not change , as light energy is conserved on reflection/refraction, the frequency also remains unchanged.

A galaxy's velocity away from us can be calculated from the shift in wavelength of a known spectral line, like sodium.

Occurs when the difference in path lengths of two waves is an integer multiple of the wavelength, resulting in a bright fringe.

Occurs when the difference in path lengths of two waves is an odd integer multiple of half the wavelength, resulting in a dark fringe.

The distance between two adjacent bright or dark fringes.

The bending and spreading of waves as they pass through an opening or around an obstacle.

Alternating bright and dark bands observed in interference patterns.

The bright fringe located at the center of the interference pattern.

A pattern of alternating bright and dark fringes formed by the superposition of two coherent waves.

x = nλD/d, where n = 0, ±1, ±2...

Light spreading out from a narrow slit or hole, appearing to bend around corners, as visualized by Newton and others.

When monochromatic light passes through a narrow slit, it creates a pattern of alternating bright and dark fringes on a screen.

The phenomena of diffraction strongly supports the wave theory of light, as it is difficult to explain with a particle model of light.

The difference in distances traveled by light waves from different parts of a slit to a point on a screen.

Different parts of the wavefront at the slit treated as independent sources emitting spherical waves in diffraction.

Characterized by a broad central bright region, flanked by weaker alternating bright and dark fringes.

The ability of an optical instrument (e.g., telescope, microscope) to distinguish fine details is limited by diffraction.

Determined by summing up the contributions from a large number of sources in the slit, accounting for their varying phases.

There's no hard distinction – it's mainly usage. Interference usually involves a small number of sources (like two slits), while diffraction arises from many sources, often a continuous wavefront.

The pattern on the screen is actually a combination of single-slit diffraction (each slit acting independently) AND double-slit interference (the waves overlapping from both slits).

The number of interference fringes within the diffraction pattern depends on the ratio of the distance between the slits (d) to the width of each slit (a).

The eyepiece's main job is to magnify the image already formed by the objective lens, providing a closer view.

Due to diffraction effects, instead of focusing to a point, the beam creates a spot of finite size. Even a perfectly corrected lens can't eliminate this.

Analysing diffraction patterns involves considering a plane wave passing through an aperture (like a slit or a circular opening). It's similar to analyzing single-slit diffraction but more complex.

The pattern formed by light waves diffracting through a circular aperture, consisting of a central bright region surrounded by concentric dark and bright rings.

The radius of the central bright region in a diffraction pattern is approximately given by r_0 ≈ 0.61λf/a, where λ is the wavelength of light, f is the focal length, and a is the aperture radius.

The ability of an optical instrument to distinguish two closely spaced objects as separate.

The minimum angular separation between two objects that can be distinguished as separate by an optical instrument.

The resolving power of an optical instrument (like a telescope or microscope) increases with the diameter of its objective lens.

The ratio of the image size to the object size in a microscope, given by m = v/f, where v is the image distance and f is the focal length.

The ability of the eye to distinguish between two closely spaced objects can be estimated by observing a pattern of black and white stripes of varying widths.

A telescope with a 100-inch objective lens (2a = 254 cm) has a limit of resolution of approximately 2.9 × 10^-7 radians when observing light with a wavelength of 6000Å.

The ability of a telescope to distinguish between two closely spaced objects as separate entities. Higher resolving power means finer details can be observed.

The minimum angular separation between two point sources that can be just resolved by a telescope or other optical instrument. This is when the center of the diffraction pattern of one source falls directly over the first minimum of the other source's pattern.

The diameter of the main lens or mirror used to gather light in a telescope or microscope.

A telescope with a larger objective lens diameter has better resolving power. Larger diameter means smaller angular separation between resolvable objects.

The minimum angular separation between two objects that the human eye can distinguish as separate. This is limited by the diffraction of light.

The ability of a microscope to distinguish between two closely spaced objects as separate entities. Limited by the diffraction of light.

By knowing the resolution of the eye and the distance at which you can clearly see a dust speck, you can estimate the size of the speck.