Light of wavelength 436 nm in air enters a fishbowl filled...

Light of wavelength $436 \mathrm{~nm}$ in air enters a fishbowl filled with water and then exits through the crown glass wall of the container. What is the wavelength of the light (a) in the water and (b) in the glass?

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Key Concepts

Refractive Index

The refractive index is a dimensionless number that indicates how much a medium slows down light compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed in the medium. This concept is central in optics for understanding how light bends and changes wavelength as it enters different materials.

Frequency Invariance

When light moves between different media, its frequency remains constant because it is determined solely by the light source. Although the speed and wavelength of light change in a new medium, the frequency does not, ensuring that the energy of the photons remains unchanged as they pass through different substances.

Wavelength Adjustment in Media

The wavelength of light in a medium is directly influenced by the medium's refractive index. Since the speed of light decreases in denser media (higher refractive index) while the frequency stays constant, the wavelength is reduced by a factor equal to the refractive index. This principle is critical in calculating the new wavelength of light as it enters materials like water or glass from air.

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