The backbone of the modern internet is made of thin strands of glass—fiber optic cables. These cables transmit data using pulses of laser light. If the light simply traveled through the glass, it would leak out the sides and the signal would be lost over short distances. However, engineers design the fiber core to have a higher index of refraction ($n_1$) than the outer cladding ($n_2$). The light enters the core at an angle greater than the critical angle ($\theta_c = \sin^{-1}(n_2/n_1)$). Because of this, the light undergoes 100% total internal reflection every time it hits the boundary, bouncing perfectly down the cable for miles without escaping.

Camera lenses, eyeglasses, and solar panels are often coated with a microscopic, ultra-thin film of transparent material (like magnesium fluoride). This is done to minimize unwanted reflections and maximize light transmission. When light strikes the coated lens, some reflects off the top of the film, and some reflects off the boundary between the film and the glass underneath. Engineers calculate the exact thickness of the film ($t = \lambda / 4n$) so that these two reflected waves undergo a $180^\circ$ phase shift relative to each other. This causes destructive interference, meaning the reflected waves cancel each other out completely, forcing all the light to transmit through the lens.

The index of refraction of diamond is $n = 2.42$. Calculate the speed of light inside a diamond. ($c = 3.0 \times 10^8 \text{ m/s}$)

A laser beam traveling through the air ($n_1 \approx 1.0$) strikes the surface of a flat piece of glass ($n_2 = 1.52$) at an angle of incidence of $45^\circ$ relative to the normal. Calculate the angle of refraction inside the glass.

What is the critical angle for light traveling from water ($n_1 = 1.33$) into air ($n_2 = 1.00$)? What happens if light hits the boundary at $55^\circ$?

Light from a red laser pointer ($\lambda = 650 \text{ nm}$) passes through two narrow slits separated by $d = 0.05 \text{ mm}$. The interference pattern is projected onto a screen $L = 2.0 \text{ m}$ away. Calculate the distance from the central maximum to the first bright fringe ($m=1$).

A thin film of oil ($n = 1.45$) floats on water ($n = 1.33$). White light shines almost perpendicularly onto the oil. What is the minimum non-zero thickness ($t$) of the oil film that will strongly reflect green light ($\lambda = 550 \text{ nm}$ in a vacuum)?

A single slit of width $a = 0.1 \text{ mm}$ is illuminated by light of wavelength $\lambda = 600 \text{ nm}$. The diffraction pattern is observed on a screen $L = 3.0 \text{ m}$ away. What is the total width of the central bright maximum?