The rectangular solid is made of two blocks of different materials: - The top block (medium 1) has thickness t = 8.69 cm and index of refraction n1 = 1.75 - The bottom block (medium 2) has thickness to = 4.95 cm and index of refraction n2 = 1.76 Suppose the word PHYSICS is written on the underside of medium 2. From above, you look straight down at the rectangular solid. How deep into the block, in cm, does the word appear to be?
The rectangular solid is made of two blocks of different materials: - The top block (medium 1) has thickness t = 8.69 cm and index of refraction n1 = 1.75 - The bottom block (medium 2) has thickness to = 4.95 cm and index of refraction n2 = 1.76 Suppose the word PHYSICS is written on the underside of medium 2. From above, you look straight down at the rectangular solid. How deep into the block, in cm, does the word appear to be?
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Transcribed Image Text:### Refraction of Light Through Parallel Layers
**Diagram 1 Explanation:**
This diagram illustrates the refraction of light as it passes through two parallel layers with different refractive indices.
- **Layers:**
- The top layer is represented with a refractive index of \( n_1 \) and is depicted as a yellow transparent medium.
- The bottom layer is shown with a refractive index of \( n_2 \) and is depicted as a gray transparent medium.
- **Incident Light:**
- The light ray enters from the air and strikes the first layer at an angle \( \theta_0 \) to the normal (perpendicular dashed line).
- **Refraction Process:**
- As the light passes from air into the first layer with refractive index \( n_1 \), it bends towards the normal.
- When the light transitions into the second layer with refractive index \( n_2 \), it refracts again, following the angle relative to the normal.
- **Pathway Measurement:**
- The light travels a distance \( D \) within the layers, with the arrows indicating the path direction and refraction changes.
This diagram serves as a fundamental representation for understanding Snell’s Law and the principles of light refraction in multi-layered media.
Transcribed Image Text:Refer to diagram 1.
The rectangular solid is made of two blocks of different materials:
- The top block (medium 1) has thickness \( t_1 = 8.69 \) cm and index of refraction \( n_1 = 1.75 \).
- The bottom block (medium 2) has thickness \( t_2 = 4.95 \) cm and index of refraction \( n_2 = 1.76 \).
Suppose the word PHYSICS is written on the underside of medium 2. From above, you look straight down at the rectangular solid. How deep into the block, in cm, does the word appear to be?
Expert Solution
Step 1
The bottom of a refracting medium appears to be elevated than actual due to refraction. This is the concept of the apparent depth (d’) and the real depth (d)
The medium’s refractive index (n) is defined as the ratio of the two as follows:
Step 2
The air has a refractive index of unity.
Let t1’ and t2’ denote the apparent depths corresponding to the given real depths t1 and t2 of the two blocks.
First, solve the apparent depth expression for the first block as follows:
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