What formula relates refractive-index ratio to depths at a plane interface?
The ratio of refractive indices equals real depth divided by apparent depth.
What conditions must hold for the real-depth/apparent-depth relation to apply?
It applies to plane surfaces with perpendicular observation and the eye in air.
How does apparent depth change when viewing from a rarer to a denser medium?
The apparent depth is smaller and the virtual image appears closer to the interface.
How does apparent depth change when viewing from a denser to a rarer medium?
The apparent depth is larger than the real depth.
How is the virtual image formed when viewing an object through a refracting interface?
The refracted ray is traced backward by the eye to form a virtual image at apparent depth.
What formula relates refractive index to real and apparent depth in air?
n = real depth ÷ apparent depth.
What is the refractive index of water used in the 24 cm container example?
4/3.
What is the real depth of water in a half-filled 24 cm container?
12 cm.
What is the apparent depth of water in a half-filled 24 cm container?
9 cm.
What equation relates real depth x and apparent depth in a 24 cm container to refractive index 4/3?
4/3 = x ÷ (24 - x).
What real depth makes a 24 cm container appear half-filled from air?
Approximately 13.72 cm.
What law and approximation lead to the apparent depth formula?
Snell’s law and sinθ ≈ tanθ approximation.
What ratio equals the refractive index in apparent depth calculation?
n ÷ 1 = AO ÷ AI.
What causes apparent displacement between an object and its image?
Refraction at an interface causes apparent displacement.
What is the formula for apparent displacement through a layer of thickness t and refractive index n?
d = t(1 - 1/n)
In a parallel-interface arrangement, how do displacement segments O₁I₁ and O₂I₂ compare?
They are equal in length.
What is the critical angle in optics?
It is the incidence angle in the denser medium where the refracted ray travels along the interface at 90°.
When does total internal reflection occur?
When light goes from a denser to a rarer medium with incidence angle above the critical angle.
What happens to the refracted angle as incidence angle approaches the critical angle?
The refracted angle increases until the ray travels along the interface at 90°.
What formula relates the critical angle to refractive indices n₁ and n₂?
sin C = n₂ / n₁
What is the critical angle formula when the rarer medium is air?
sin C = 1 / n
Which factors affect the critical angle for light?
The denser medium, the rarer medium, and the light's colour
Why is the glass–air critical angle about 42° for yellow light?
Because sin C = 1 / (3/2) = 2/3
What is the approximate water–air critical angle for yellow light?
About 48°35′
What formula gives the water–air critical angle as about 48°35′?
sin C = 1 / (4/3) = 3/4
What is the critical angle for the glass–water pair?
Approximately 62°44′
How is the glass–water critical angle calculated?
sin C = (4/3) / (3/2) = 8/9
Pon a prueba tus conocimientos con 13 preguntas sobre Apparent Depth and Total Internal Reflection.
1. Light travels from a medium with refractive index n₁ to a rarer medium with refractive index n₂; which expression gives the critical angle C?
2. What is the critical angle for light traveling from a denser medium into a rarer medium?
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