A glass optical fiber (n = 1.50) is submerged in water (n = 1.33). What is the critical angle for light to stay inside the fiber?

The index of refraction for violet light in silica flint glass is $n_V$, and that for red light is $n_R$. What is the angular spread of visible light passing through a prism of apex angle $\Phi$ if the angle of incidence is $\theta$? as we discussed earlier?

A submarine is $300 \mathrm{~m}$ horizontally from the shore of a GP freshwater lake and $100 \mathrm{~m}$ beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water $210 \mathrm{~m}$ from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level.
(c) Find the angle of refraction.

The speed of a water wave is described by $v=\sqrt{g d}$, where $d$ is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth. Suppose waves approach the coast, carrying energy with uniform density along originally straight wave fronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays.

A submarine is $300 \mathrm{~m}$ horizontally from the shore of a GP freshwater lake and $100 \mathrm{~m}$ beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water $210 \mathrm{~m}$ from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level.
(b) Find the angle of incidence of the beam striking the water-air interfa

The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular spread of visible light passing through a prism of apex angle $60.0^{\circ}$ if the angle of incidence is $50.0^{\circ}?$

Two light pulses are emitted simultaneously from a source. Both pulses travel through the same total length of air to a detector, but mirrors shunt one pulse along a path that carries it through an extra length of 6.20 m of ice along the way. Determine the difference in the pulses’ times of arrival at the detector.

A submarine is 300 m horizontally from the shore of a freshwater lake and 100 m beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water 210 m from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level. (a) Draw a diagram of the situation, identifying the two triangles that are important in finding the solution. (b) Find the angle of incidence of the beam striking the water–air interface. (c) Find the angle of refraction. (d) What angle does the refracted beam make with the horizontal? (e) Find the height of the target above sea level.

The speed of a water wave is described by $v=\sqrt{g d}$, where d is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth. Sketch a map of an ocean beach on the eastern side of a landmass. Show contour lines of constant depth under water, assuming reasonably uniform slope. Sketch a map of a coastline with alternating bays and headlands, as suggested in the given figure. Again make a reasonable guess about the shape of contour lines of constant depth. Suppose that waves approach the coast, carrying energy with uniform density along originally straight wavefronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays.

In each of the following situations, a wave passes through an opening in an absorbing wall. Rank the situations in order from the one in which the wave is best described by the ray approximation to the one in which the wave coming through the opening spreads out most nearly equally in all directions in the hemisphere beyond the wall.
(a) The sound of a low whistle at $1 \mathrm{kHz}$ passes through a doorway $1 \mathrm{~m}$ wide.
(b) Red light passes through the pupil of your eye.
(c) Blue light passes through the pupil of your eye.
(d) The wave broadcast by an AM radio station passes through a doorway $1 \mathrm{~m}$ wide.
(e) An x-ray passes through the space between bones in your elbow joint.

The speed of a water wave is described by $v=\sqrt{g d}$, where d is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth. Sketch a map of an ocean beach on the eastern side of a landmass. Show contour lines of constant depth under water, assuming reasonably uniform slope. Suppose that waves approach the coast from a storm far away to the north-northeast. Demonstrate that the waves will move nearly perpendicular to the shoreline when they reach the beach.

The speed of a water wave is described by , where d is the water depth, assumed to be small compared to the wavelength. Because their speed changes, water waves refract when moving into a region of different depth. (a) Sketch a map of an ocean beach on the eastern side of a landmass. Show contour lines of constant depth under water, assuming a reasonably uniform slope. (b) Suppose waves approach the coast from a storm far away to the north–northeast. Demonstrate that the waves move nearly perpendicular to the shoreline when they reach the beach. (c) Sketch a map of a coastline with alternating bays and headlands. Again make a reasonable guess about the shape of contour lines of constant depth. (d) Suppose waves approach the coast, carrying energy with uniform density along originally straight wave fronts. Show that the energy reaching the coast is concentrated at the headlands and has lower intensity in the bays. $v = \sqrt { g d }$

A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of $50.0^{\circ}$. The index of refraction of quartz is 1.455 at 600 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.

Find the Maclaurin series for the function. f(x) = {arcsin x / x, x ≠ 0 {1, x = 0