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Chapter 9: Problem 33

Explain why images seen through flat, smooth, uniform, plate-glass windows are undistorted.

Short Answer

Expert verified
Answer: Images seen through flat, smooth, uniform, plate-glass windows are undistorted because the windows have a consistent refractive index, allowing light to pass through with minimal refraction and bend in a consistent way. The uniformity and flatness of the glass ensure that the light rays maintain their original paths and relative angles, preserving the image's integrity.

Step by step solution

01

Understand the properties of light

Light travels in straight lines through homogeneous media, which means that it doesn't change direction in a medium with consistent properties. However, when light passes from one medium to another, such as from air to glass, its direction might change due to a phenomenon called refraction. The amount by which light bends is determined by the refractive indices of the two media and the angle at which the light enters the new medium.
02

Introduce the concept of refraction

Refraction is the bending of light as it passes from one medium to another with a different refractive index. The refractive index is a measure of how much light slows down in the medium. When light passes from a medium with lower refractive index to one with a higher refractive index, it bends towards the normal (a line perpendicular to the surface), and when it passes from a medium with a higher refractive index to one with a lower refractive index, it bends away from the normal. The angle of refraction depends on the refractive indices of the two media and the angle of incidence.
03

Describe the uniformity of plate-glass windows

Plate-glass windows are smooth, flat, and uniform, which means they have a consistent refractive index throughout. This uniformity ensures that any light passing through the glass will be refracted in the same way and by the same amount, regardless of where it enters the glass.
04

Explain why images are undistorted through plate-glass windows

Since plate-glass windows are flat, when light enters the glass perpendicular to the surface, the angle of incidence is zero degrees, and there is no refraction. As a result, the light travels straight through the glass without changing direction. Moreover, the uniform refractive index ensures that the light exits the glass and enters back into the air in a consistent manner, meaning that light rays entering the glass at the same angle will exit at the same angle, preserving the angles and relationships between light rays in the image. In other words, the image remains undistorted because the light rays are not scattered or bent in irregular ways as they pass through the glass.
05

Summarize the explanation

To recap, images seen through flat, smooth, uniform, plate-glass windows are undistorted because the windows have a consistent refractive index, allowing light to pass through with minimal refraction and bend in a consistent way. The uniformity and flatness of the glass ensure that the light rays maintain their original paths and relative angles, preserving the image's integrity.

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