Ch 31: Geometric OpticsWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Refraction of Light

Concept #2: Snell's Law

Practice: A light ray passes from air to glass, with an index of refraction of 1.5. If the light if blue, with a wavelength of 450 nm, what is the wavelength of the light ray after it passes into the glass?

Example #1: Refraction Through Multiple Boundaries

Additional Problems
Light passes from air into some other medium. The light enters with an incident angle of 40o and a wavelength of 425 nm, and passes through the boundary with some refracted angle of 30o. What is the wavelength of the light in the medium? Assume all angles are measured with respect to the normal of the boundary. 
A tank holds a layer of oil, 1.65 m thick, which floats on a layer of syrup that is 0.83 m thick as shown in the figure. Both liquids are clear and do not intermix. A ray, which originates at the bottom of the tank on a vertical axis, crosses the oil-syrup interface at a point 0.90 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m from the axis and at the critical angle. Find the index of refraction of the syrup.
The figure shows the path of a portion of a ray of light as it passes through three different materials. Note: The figure is drawn to scale. What can be concluded concerning the refractive indices of these three materials? a. n1 < n2 < n3 b. n1 > n2 > n3 c. n3 < n1 < n2 d. n2 < n1 < n3 
The index of refraction for red light in water is 1.331 and that for blue is 1.340. If the incident angle of a white light beam is 83°, what is the angle between the red and blue light inside water? a. 0.22° b. 0.75° c. 0.43° d. 0.36°
A prism with angles of 60°-60° -60° and refractive index of 1.6 is partially immersed in an oil with n=1.2 as shown. A light beam entering from air at the top (P) strikes point Q at the critical angle. Find the incident angle θ. a. 27.0° b. 16.5° c. 18.5° d. 11.4°
Light in air is shone on the surface of oil with an index of refraction of 1.25. Beneath the layer of oil is water, which has an index of refraction of 1.33. If the light travels through the water with an angle of 32° from the normal, at what angle (measured from the normal) was the light incident on the oil with?  
Consider a spherical rain drop in the air. A laser beam is directed at the rain drop from the left and slightly above the central axis (see figures). Which of the following diagrams best indicates the trajectory of the light? (Note, the dotted lines cross in the center of each drop, and therefore indicate the normal to the surface.)
Light goes from flint glass into ethanol. The angle of refraction in the ethanol is 24.8°, the index of refraction for flint glass is 1.61, and the index of refraction for ethanol is 1.36. What is the angle of incidence in the glass? 1. 10.8702 2. 12.7958 3. 20.4236 4. 21.3253 5. 18.6127 6. 20.7518 7. 16.378 8. 17.6211 9. 9.6954 10. 12.3777
A ray of light traveling in material a strikes the interface between materials  a and b and refracts into material b. In material a, the light makes an angle of 30° with respect to the surface of material a and in material b, it makes an angle of 60° with respect to the surface of material  b. Which of the following statements is correct? (a) The light travels faster in material b than in material a. (b) The light travels slower in material b than in material a. (c) The speed of the light is the same in both materials.
A person in the air above the water in a swimming pool looks straight down into the water (n = 1.33) at a diamond ring that lies on the bottom of the pool. If the image of the ring is 1.20 m below the surface of the water, what is the depth of the water (the distance from the surface of the water to the bottom of the pool)? Hint: Assume θ<<1, so sinθ=θ, and tanθ=θ, for a θ in radians. (a) 0.60 m (b) 0.90 m (c) 1.20 m (d) 1.60 m (e) 2.40 m (f) none of the above answers
A light beam shown in the figure makes an angle of 30° with the normal to the air-oil surface. Determine the angle θ.a. 22.2°b. 24.7°c. 40.5°d. 37.0°
Light of wavelength 475nm in vacuum enters a plastic as shown in Fig. 1. Measurements of the light in the plastic indicate that its wavelength there is 394 nm. What is the frequency of the light in the plastic? 
Consider a light ray which enters from air to a liquid, where the index of refraction of the liquid is given by n = √2. Denote the wavelength and the frequency in the liquid by ⋋′ and f′ and those in the air by ⋋ and f. Choose the correct pair of ratios: 1. ⋋' / ⋋ = √2, f' / f = √2 2. ⋋' / ⋋ = 1, f' / f = √2 3. ⋋' / ⋋ = 1/2, f' / f = 1 4. ⋋' / ⋋ = 1/√2, f' / f = 1 5. ⋋' / ⋋ = 2, f' / f = √2 6. ⋋' / ⋋ = 1/2, f' / f = √2 7. ⋋' / ⋋ = 1, f' / f = 1 8. ⋋' / ⋋ = 2, f' / f = 1 9. ⋋' / ⋋ = 1/√2, f' / f = √2 10. ⋋' / ⋋ = √2, f' / f = 1
Light of wavelength 475nm in vacuum enters a plastic as shown in Fig. 1. Measurements of the light in the plastic indicate that its wavelength there is 394 nm. At what direction does the light travel with respect to the normal in the plastic?
A narrow beam of light passes through a plate of glass with thickness 1.03 cm and a refractive index 1.46. The beam enters from air at an angle 20.1°. The goal is to calculate the deviation d of the ray as indicated in the figure. Find deviation d.
Light of wavelength 862 nm is incident on the face of a silica prism at an angle of θ  1 = 74.1° (with respect to the normal to the surface). The apex angle of the prism is ∅ = 53.8°. Given: The value of the index of refraction for silica is n = 1.455. Find the angle of refraction at this first surface.
As shown at right below, a laser is directed into a water tank (filled with water having an index of refraction n2 at the laser wavelength) at an angle  θ1 from the vertical and strikes the bottom of the tank at point A, a horizontal ditance r away from B, the spot directly underneath the place where the light enters the water. The distance r is:
As shown at right below, a laser is directed into a water tank (filled with water having an index of refraction n2 at the laser wavelength) at an angle  θ1 from the vertical and strikes the bottom of the tank at point A, a horizontal ditance r away from B, the spot directly underneath the place where the light enters the water. The index of refraction of water for red light is 1.331, while the index of refraction of water for green light is 1.336. The angle of refraction θ2 would bea) the same for a green and a red laser.b) smaller for a red laser than for a green laser.c) smaller for a green laser than for a red laser.
A beam of white light is incident on a triangular glass prism with an index of refraction of about 1.5 for visible light, producing a spectrum. Initially, the prism is in a glass aquarium filled with air, as shown. If the aquarium is now filled with water, with an index of refraction of 1.3, which of the following is true? 1. The spectrum produced has greater separation between red and violet than that produced in air. 2. A spectrum is produced, but the deviation of the beam is opposite to that seen in air. 3. The spectrum has the same separation between red and violet as that produced in air. 4. Violet light will not emerge from the prism. 5. The intensity of the light emerging increases. 6. There is no light seen coming out of the prism. 7. The spectrum produced has less separation between red and violet than that produced in air. 8. The positions of red and violet are reversed in the spectrum. 9. No spectrum is produced. 10. Red light will not emerge from the prism.
Light strikes a glass plate at an angle of incidence of 60 degrees. Part of the beam is reflected and part is refracted. It is observed that the reflected and refracted rays are perpendicular to each other. What is the index of refraction of the glass?
A ray of light traveling in air is incident on the surface of a block of clear ice (of index 1.309) at an angle of 43.4° with the normal. Part of the light is reflected and part is refracted. Find the angle between the reflected and the refracted light. Answer in units of °.
A submarine is 400 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 300 m from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. Recall, the index of refraction of water is 1.33. Find the height of the target above the level of the water.