In Example 33.11, the water-glass interface is horizontal. If instead this interface were tilted 15.0° above the horizontal, with the right side higher than the left side, what would be the angle from the vertical of the ray in the glass? (The ray in the water still makes an angle of 60.0° with the vertical).
EXAMPLE 33.11: Reflection and refraction
In Fig 33.11, material a is water and material b is a glass with an index of refraction 1.52. If the incident ray makes an angle of 60.0° with the normal, find the directions of the reflected and refracted rays.
SOLUTION
IDENTIFY: This is a problem in geometric optics. We are given the incident angle and the index of refraction of each material, and we need to find the reflected and refracted angles.
SET-UP: Figure 33.11 shows the rays and angles for this situation. The target variables are the reflected angle θr and the refracted angle θb. Since nbis greater than na, the refracted angle must be smaller than the incident angle θa; this is shown in the figure.
EXECUTE: According to Eq 33.2, the angle the reflected ray makes with the normal is the same as that of the incident ray so θr= θa=60.0°.
To find the direction of the refracted ray, we use Snell’s law, Eq 33.4, with na=1.33, nb=1.42, and θa=60.0°. We find:
EVALUATE: The second material has a larger refractive index than the first, just like the situation shown in Fig 33.8a. Hence, the refracted ray is bent toward the normal as the wave slows down upon entering the second material and θb< θa.
Figure 33.11. Reflection and refraction of light passing from water to glass
Figure 33.8. Reflection and refraction in three cases. (a) Material b has a larger index of refraction than material a. (b) (a) Material b has a smaller index of refraction than material a. (c) The incident light ray is normal to the interface between the materials.
5) A light ray incident on a block of glass makes an incident angle of 50.0° with the normal to the surface. The refracted ray in the block makes a 26.8° with the normal. What is the index of refraction of the glass?
6)
A light ray traveling from a higher index of refraction medium into a lower index of refraction medium (for example, from water into the air) would bend away from the normal to the medium surface. When the refracted ray is parallel to the boundary of the medium, θ2= 90°. The incident angle, θ1, becomes θc, called the
