A beam of light consisting of a mixture of red, yellow, and...

A beam of light consisting of a mixture of red, yellow, and blue light originates from a source submerged in some carbon disulfide. The light beam strikes an interface between the carbon disulfide and air at an angle of incidence of $37.5^{\circ}$ as shown in the figure. The carbon disulfide has the following indices of refraction for the wavelengths present: red $(656.3 \mathrm{~nm}), n=1.6182 ;$ yellow $(589.3 \mathrm{~nm}), 1.6276 ;$ blue $(486.1 \mathrm{~nm}), 1.6523 .$ Which color(s) is/are recorded by the detector located above the surface of the carbon disulfide?

A beam of light consisting of a mixture of red, yellow, and blue light originates from a source submerged in some carbon disulfide. The light beam strikes an interface between the carbon disulfide and air at an angle of incidence of $37.5^{\circ}$ as shown in the figure. The carbon disulfide has the following indices of refraction for the wavelengths present: red $(656.3 \mathrm{~nm}), n=1.6182 ;$ yellow $(589.3 \mathrm{~nm}), 1.6276 ;$ blue $(486.1 \mathrm{~nm}), 1.6523 .$
Which color(s) is/are recorded by the detector located above the surface of the carbon disulfide?

Key Concepts

Dispersion

Dispersion refers to the dependence of the refractive index on the wavelength of light. As a result, different colors (or wavelengths) of light bend by different amounts when they refract. This leads to effects such as the separation of colors in prisms, and in practical scenarios, it determines which wavelengths might undergo total internal reflection based on their specific refractive indices.

Snell's Law

Snell’s Law relates the index of refraction of two media with the sine of the angles of incidence and refraction. It governs how light refracts, or bends, when transitioning from one medium to another, and is expressed as n1*sin(?1) = n2*sin(?2). This fundamental principle is crucial for calculating the change in light direction based on different refractive indices.

Critical Angle

The critical angle is the minimum angle of incidence for which light, traveling from a denser medium to a less dense medium, is completely reflected back into the original medium rather than refracted. It is defined by the relationship sin(?c) = n2/n1, where n1 is the refractive index of the denser medium and n2 that of the less dense medium. If the angle of incidence exceeds this critical angle, total internal reflection occurs.

Total Internal Reflection

Total internal reflection is the phenomenon where all of the incident light is reflected back into the optically denser medium when the angle of incidence exceeds the critical angle. This concept is essential in understanding scenarios where light does not pass into the second medium, which directly affects which wavelengths are observed in a system.

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