Exam 32: The Nature and Propagation of Light

In the figure, the orientation of the transmission axis for each of three polarizing sheets is labeled relative to the vertical direction. A beam of light, polarized in the vertical direction, is incident on the first polarized with an intensity of 1000 W/m². What is the intensity of the beam after it has passed through the three polarizing sheets when θ₁ = 30°, θ₂ = 30° and θ₃ =60°?

Polarized light passes through a polarizer. If the electric vector of the polarized light is horizontal what, in terms of the initial intensity I₀, is the intensity of the light that passes through a polarizer if the polarizer is tilted 22.5° from the horizontal?

An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)

A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O crosses the brine-oil interface at a point 0.60 m from the axis. The ray continues and emerges into the air above the oil. What is the angle that the ray in the air makes with the vertical?

A ray of light traveling in air strikes the surface of a certain plastic slab at 63.0° with respect to the normal in air. It travels in the plastic slab at a 30.6° angle with respect to the normal. Find the critical angle for the plastic in air.

The following are positioned in sequence: A source of a beam of natural light of intensity I₀; three ideal polarizers A, B, and C; and an observer. Polarizer axis angles are measured clockwise from the vertical, from the perspective of the observer. The axis angle of polarizer A is set at 0° (vertical), and the axis angle of polarizer C is set at 50°. Polarizer B is set so that the beam intensity is zero at the observer. Which of the following pairs of angles are possible axis angle settings of polarizer B?

The speed of light in a material is 0.50c. What is the critical angle of a light ray at the interface between the material and a vacuum?

A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)