A step-index optical fiber guides light in a higher-index core surrounded by a lower-index cladding. Explain the geometric-optics condition for total internal reflection and why the incident angle must be measured from the normal.

An anti-reflective coating is designed so that the two dominant reflected waves interfere destructively near a target wavelength. Explain why optical path difference and reflection phase shifts both matter.

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.

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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 $55^\circ$?

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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 ($m=1$).

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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)?

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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?

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A thin converging lens has focal length $f=10\text{ cm}$. An upright object $4.0\text{ cm}$ high is placed $30\text{ cm}$ in front of the lens. Determine the image distance, image height, and whether the image is real or virtual.

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