Chapter 34: Problem 9
A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 cm. Reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.00 cm behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.
Short Answer
Step by step solution
Understand the given values and formula needed
Substitute known values to find object distance
Calculate the magnification and image size
Determine the orientation and nature of the image
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Convex Surfaces
These types of mirrors give a wide field of view, which is why they are commonly used as rearview mirrors in vehicles. Key characteristics of images formed by convex mirrors include:
- Images are always smaller than the actual object.
- Images are virtual, meaning they cannot be projected.
- Images are upright, appearing the same way up as the object.
Mirror Equation
- \( f \) is the focal length,
- \( o \) is the object distance (distance from the object to the mirror),
- \( i \) is the image distance (distance from the image to the mirror).
Virtual Images
These images are always formed on the side opposite to where the object exists. They appear to originate from a point behind the mirror where the reflected rays seem to diverge. For our specific problem with the coin and the spherical glass shell, the image is virtual because:
- The image distance is negative.
- The light rays are diverging.
- It appears upright and smaller.
Magnification
- \( m \) is the magnification,
- \( i \) is the image distance, and
- \( o \) is the object distance.
Optics
- Understanding light reflection and refraction processes.
- Applying formulas like the mirror equation to practical tasks.
- Exploring how lenses and mirrors alter visual perception.