Figure P 35.45 shows a desk ornament globe containing a...

Figure $\mathrm{P} 35.45$ shows a desk ornament globe containing a photograph. The flat photograph is in air, inside a vertical slot located behind a water-filled compartment having the shape of one half of a cylinder. Suppose you are looking at the center of the photograph and then rotate the globe about a vertical axis. You find that the center of the photograph disappears when you rotate the globe beyond a certain maximum angle (Fig. P35.45b). Account for this phenomenon and calculate the maximum angle. Briefly describe what you would see when you turn the globe beyond this angle.

Figure $\mathrm{P} 35.45$ shows a desk ornament globe containing a photograph. The flat photograph is in air, inside a vertical slot located behind a water-filled compartment having the shape of one half of a cylinder. Suppose you are looking at the center of the photograph and then rotate the globe about a vertical axis. You find that the center of the photograph disappears when you rotate the globe beyond a
certain maximum angle (Fig. P35.45b). Account for this phenomenon and calculate the maximum angle. Briefly describe what you would see when you turn the globe beyond this angle.

Key Concepts

Snell's Law

Snell's Law describes how light rays change direction when passing from one medium to another with a different refractive index. It quantitatively relates the sine of the angle of incidence to the sine of the angle of refraction via the refractive indices of the two media. This law is fundamental in understanding how light bends at the boundary between water and air, which in this case affects how the image of the photograph is seen or lost as the viewing angle changes.

Total Internal Reflection and Critical Angle

When light travels from a medium with a higher refractive index to one with a lower index, there exists a specific angle of incidence—the critical angle—beyond which light cannot exit the medium but is instead completely reflected internally. This phenomenon, known as total internal reflection, explains why, upon rotating the globe beyond a maximum angle, the light rays from the center of the photograph fail to emerge from the water-filled compartment. The disappearance of the photograph’s center is due to the incident rays hitting the water–air interface at angles exceeding this critical value.

Refraction at Curved Interfaces

In the context of the globe ornament, the water compartment’s curved (cylindrical) interface complicates the usual refraction process since the normal to the surface changes at every point. The curvature means that the path of light rays from the photograph is altered in a way that depends not only on the angle of incidence but also on the point of entry on the curved surface. Analyzing the geometry of this curved interface in combination with Snell’s Law clarifies how the viewing angle is limited and provides the basis for calculating the maximum angle at which the photograph remains visible.

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