Problem 16
A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of \(\theta_a = 36.2{^\circ}\), the ray refracted into the water makes an angle of 49.8\(^\circ\) with the normal to the interface. What is the smallest value of the incident angle \(\theta_a\) for which none of the ray refracts into the water?
Problem 17
The critical angle for total internal reflection at a liquid air interface is 42.5\(^\circ\). (a) If a ray of light traveling in the liquid has an angle of incidence at the interface of 35.0\(^\circ\), what angle does the refracted ray in the air make with the normal? (b) If a ray of light traveling in air has an angle of incidence at the interface of 35.0\(^\circ\), what angle does the refracted ray in the liquid make with the normal?
Problem 18
A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. (a) If the cube is in air, at what minimum angle with the normal inside the glass will this light \(not\) enter the air at this surface? (b) What would be the minimum angle in part (a) if the cube were immersed in water?
Problem 19
A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass-water interface at an angle to the normal larger than 48.7\(^\circ\), no light is refracted into the water. What is the refractive index of the glass?
Problem 22
The indexes of refraction for violet light \((\lambda = 400 \, \mathrm{nm})\) and red light \((\lambda = 700 \, \mathrm{nm})\) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5\(^\circ\) to the normal. Calculate the angular separation between these two colors of light in the refracted ray.
Problem 25
Unpolarized light with intensity \(I_0\) is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0\(^\circ\) with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed through the second filter?
Problem 26
(a) At what angle above the horizontal is the sun if sunlight reflected from the surface of a calm lake is completely polarized? (b) What is the plane of the electric-field vector in the reflected light?
Problem 29
A parallel beam of unpolarized light in air is incident at an angle of 54.5\(^\circ\) (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. (a) What is the refractive index of the glass? (b) What is the angle of refraction of the transmitted beam?
Problem 30
The refractive index of a certain glass is 1.66. For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in (a) air and (b) water?
Problem 31
A beam of polarized light passes through a polarizing filter. When the angle between the polarizing axis of the filter and the direction of polarization of the light is \(\theta\), the intensity of the emerging beam is \(I\). If you now want the intensity to be \(I/2\), what should be the angle (in terms of \(\theta\)) between the polarizing angle of the filter and the original direction of polarization of the light?
