Commented Resolution

Geometric Optics

Spherical Mirrors (2)

 

01- According to the statement, the metamaterial presents properties and behaviors that are not found in natural materials — therefore, the only alternative that can represent the refraction of light when passing into the metamaterial is D, which cannot happen because the incident and refracted light rays must be in opposite quadrants —   R- D  

Note: Note in the figures below that, in natural materials, in homogeneous media and

transparent occurs in addition to refraction (which predominates), reflection and absorption — also note that in reflection the incident and reflected rays are in adjacent quadrants, and that in refraction the incident and refracted rays are in opposite quadrants (figure 1) — in absorption the incident ray is absorbed (figure 2).

02- As the rays penetrate the frosted glass, refraction occurs and as the rays cease to be 

parallel, they spread (diffuse) inside and provide an observer on the other side of the glass with a distorted image or just its contours, as you can see in the murder scene in the bathroom in Alfred Hitchcock’s classic film Psycho (figure above). 

R-C

03- There are infinite frequencies (colors) that make up the white polychromatic light coming from 

Sun.

R-D

04- Light dispersion is the phenomenon of separation of white polychromatic light into its component colors, which occurs when white light undergoes refraction, for example, in a glass prism (figure 1) or in water drops (figure 2) — white polychromatic light is composed of infinite 

colors (frequencies), of which we highlight red, orange, yellow, green, blue, indigo and violet — note in figure 1 that the color that undergoes the least deviation is red and the one that undergoes the greatest deviation is violet — R- A

05- During the day, refraction predominates, as the amount of external light is greater than that of internal light, and at night, reflection predominates, as the amount of external light is less than that of internal light —  R- C   

06- I- False — the polychromatic white light from the Sun hits a drop of water in the air (1) and, upon penetrating it, undergoes refraction provided by the law of refraction n ₁ .seni = n ₂ .senr, also suffering a small dispersion (almost imperceptible) of the colors that make up the white light — these rays of light of the different colors reflect on the inside of the drop (2) and return maintaining their colors — upon undergoing the last refraction (3), leaving the drop and increasing the separation between the colors — it is these more separated colors that reach your eyes and make you see the rainbow — in 

In the figure (primary rainbow, with only one internal reflection), only the extreme colors, red and violet, are represented — note that the diffraction that makes up the rainbow occurs in situations 1 and 3.

Note: In the primary rainbow, the light undergoes only one internal reflection (figure I) and the extreme color i

The interior will be violet — in the secondary rainbow the light undergoes two internal reflections (figure II) and the extreme interior color will be red.

II- Correct — it can occur naturally in raindrops and artificially when, for example, light is decomposed in a prism.

III- False — note in explanation I that the greatest dispersion of colors, which form the rainbow, occurs when the light leaves the drop and passes into the air and not inside the drop.

IV- Correct — it is due to the passage of light through rain droplets that the dispersion of light and the formation of the rainbow occur.

R-B

07- As the atmosphere is denser in the lower layers, the refractive index is greater in them. 

in the upper layers and the ray of light, as it descends, passes from a less refractive medium to a more refractive medium — thus, it gets closer and closer to the normal, curving as shown in the figure above —   R- C

08- The Sun in contact with the ground makes the air hotter and consequently less refractive than the air in the upper layers. This causes the light rays to undergo total reflection in layers close to the ground, rise and reach the eyes of an observer, who will have the impression that there is a mirror on the ground providing the image of the object —  R- B 

09- Observe in the figure below, that in the dispersion of sunlight that causes the rainbow, the light returns to the 

original medium and for this to happen the Sun has to be behind the observer —  R- D 

10- n _glass = c / V _glass   — 1.5 = 3.10 ⁸ / V _glass   — V _glass = 2.10 ⁸ m / s — f = V / λ — as the frequency f is independent of the propagation medium — f _air = f _glass   — λ _air = 600nm = 6.10 ² .10 ^-9 = 6.10 ^-7 m — f _air = f _glass   — V _air / γ _air  = V _glass / γ _glass   — 3.10 ⁸ / 6.10 ^-7 = 2.10 ⁸ / λ _glass   — λ _glass = 4.10 ^-7   — γ _glass = 400.10 ^-9   — λ _glass = 400nm —  R – E  

11- Observe the figure below — as the rays of light coming from the Sun penetrate the 

Earth’s atmosphere, encounter increasingly denser, more refractive layers of air with higher refractive indices and approach the normal more and more, suffering the deviations shown — these deviations cause the image of the Sun observed at dawn (before the object Sun appears) and at dusk (after the object Sun has disappeared) to be above its real position, taking the horizon as a reference. —  R-C 

12- Tracing the normal N at the point of incidence (the normal N forms an angle of 90 ^°  with the 

glass surface) — note in the figure that the angle of incidence, which is the angle that the incident ray forms with the normal, is i=(90 – 32)=58 ^o   — i=58 ^o   — also note that 58 ^o  + r=90 ^o   — r=32 ^o   —  R- B 

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