Quick questions on Refraction, Snell's law and dispersion: VCE Physics Unit 4

1. Light must travel from a denser medium to a less dense medium ($n_1 > n_2$). 2. The angle of incidence must exceed the critical angle ($\theta_1 > \theta_c$).

Diamond's very small critical angle is the reason for its sparkle: light entering from above is internally reflected many times before exiting through specific facets at the bottom.

A glass prism refracts light entering one face and refracts it again on exit. Because different colours have different $n$, they bend by different amounts, and the prism separates white light into a spectrum.

A rainbow is dispersion in raindrops. Sunlight enters a spherical raindrop, refracts (with dispersion), reflects off the back of the drop, and exits refracting again. Different colours emerge at slightly different angles, producing the familiar arc with red on the outside (42 degrees from the antisolar point) and violet on the inside (40 degrees).

Single-element lenses (like a magnifying glass) suffer from chromatic aberration: different colours focus at slightly different points because their refractive indices differ. Camera and microscope lenses correct this with multiple elements made of different glass types.

Light in air ($n_1 = 1.00$) hits glass ($n_2 = 1.50$) at 45 degrees.

Light in water ($n_1 = 1.33$) hits the surface at 50 degrees.

A glass block has $n_{\text{red}} = 1.50$ and $n_{\text{violet}} = 1.55$. Light enters at 45 degrees. Find the angles of refraction for red and violet.

A thin glass or plastic core (high $n$) surrounded by a cladding (lower $n$). Light entering the core at sufficiently grazing angle reflects off the core-cladding boundary at angles greater than $\theta_c$, so all light remains trapped in the core as it travels along the fibre. Used for high-bandwidth communications (internet, telephony) and medical endoscopes.

Right-angle prisms can be used as 100 percent efficient reflectors at angles where the light hits the back face at greater than $\theta_c$. Used in binoculars, periscopes, and reflex cameras.

Hot air near a road has lower density and lower $n$ than air above. Light from the sky bends as it traverses the density gradient, and at very grazing angles undergoes effective TIR off the hot air layer, creating an apparent puddle.

$n_1 \sin \theta_1 = n_2 \sin \theta_2$. A common slip is to write $\sin \theta_1 / \sin \theta_2 = n_2 / n_1$ (inverted ratio).

$\theta_c$ is computed from $\sin \theta_c = n_2 / n_1$ where $n_1 > n_2$. It is the threshold angle of incidence at which TIR begins.

TIR only occurs going from denser to less dense ($n_1 > n_2$). It cannot occur going from air into glass.

Snell's law uses angles from the normal (perpendicular to the surface), not from the surface itself.