Dispersion, Apparent Depth, and Multi-Step Reasoning Quiz

Different wavelengths travel at different speeds in a material. The concept is dispersion, meaning refractive index varies with wavelength.

Shorter wavelengths usually experience a slightly higher refractive index. The concept is dispersion, where blue (shorter wavelength) bends more due to higher n.

Wavelength-dependent refraction separates colours. The concept is dispersion in a prism, producing different bending for different wavelengths.

Water to air (lower n) causes bending away from the normal. The concept is refraction away from the normal when entering a lower refractive index medium.

For small viewing angles, the apparent depth of an object when viewed through a medium is affected by the refractive index of that medium. The relationship shows that as the refractive index increases, the apparent depth decreases relative to the real depth. This phenomenon occurs due to the bending of light as it passes through different media, causing the object to appear shallower than it actually is. Thus, the formula d_app ≈ d/n captures this relationship, where d_app is the apparent depth, d is the real depth, and n is the refractive index.

15/1.33 ≈ 11.3cm. The concept is apparent depth calculation, using d_app ≈ d/n.

Frequency is set by the source; the medium changes speed and wavelength. The concept is constant frequency across a boundary, combined with v=fλ for wavelength change.

v=fλ; lower v means lower λ. The concept is the wave equation (v=fλ), linking slower speed to shorter wavelength.

Snell: n_1 sin(θ_1)=n_2 sin(θ_2). Rearranging gives sin(θ_2)=(n_1/n_2)sin(θ_1). The concept is Snell's law, used to compute refraction angles.

sin(25°)≈0.423, close to 0.429. The concept is trig estimation, choosing the angle with sine closest to the computed value.

Snell's law gives a consistent relationship. For fixed n_1 and n_2, larger sin(θ_1) leads to larger sin(θ_2). The concept is Snell's law monotonic relationship.

sin(θ_c)=0.67 corresponds to about 42°. The concept is critical angle, found from sin(θ_c)=n_2/n_1.

a, b, d are correct. The concept is total internal reflection, where beyond θ_c, Snell's law would require sin(θ_2)>1 so transmission cannot occur.

55° > 49° → TIR. The concept is the critical angle test, comparing θ_1 to θ_c.

Mirages occur when light rays bend as they pass through layers of air at different temperatures. On hot roads, the air close to the surface is significantly warmer than the air above it. This temperature gradient causes light to refract, leading to the illusion of water or a reflective surface. As light travels from cooler to warmer air, it bends upward, creating the characteristic shimmering effect that resembles a pool of water on the road. Thus, the phenomenon is directly linked to variations in air temperature.

It’s refraction in a gradient medium, not a single boundary. The concept is continuous refraction, caused by a refractive index gradient.

Different speeds → different refractive indices → different bending. The concept is dispersion, linking wavelength to refractive index and refraction angle.

v=c/n. Increasing n reduces v. The concept is refractive index definition, showing how speed changes in media.

Fermat’s principle provides a deeper explanation of refraction. The concept is Fermat’s principle, which says light follows the path of least time.

Those are the main quantitative and conceptual tools. The concept is Snell’s law + refractive index, with key extensions dispersion, apparent depth, and total internal reflection.