Researchers studying coastal waters wish to determine the optical properties of a…
PHYSICS · Multi-part · CBSE · Physics · Ray Optics and Optical Instruments · Ray Optics and Optical Instruments
Problem
Researchers studying coastal waters wish to determine the optical properties of a sample of seawater. They insert one end of an optical fiber into the seawater and gradually tilt the fiber until light emerging inside the water no longer passes into the surrounding air. The largest angle of incidence inside the seawater for which light still emerges into air is measured to be 42∘ (uncertainty ±1∘). Take the index of refraction of air to be 1.00.
(a) Calculate the index of refraction of the seawater based on the measured critical angle, expressing the result with appropriate significant figures.
(b) Using your value from part (a), determine the speed of light in the seawater.
(c) Green light in air has a wavelength of 530nm. Compute its wavelength in the seawater sample.
(d) Determine the absolute uncertainty in the index of refraction arising from the ±1∘ uncertainty in the critical angle. Clearly state your reasoning.