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Exercise for Submission: Part 1: Refraction is the binding of a light ray as it passes from one medium to another, for instance from air to water. This phenomenon is why your straw appears to be distorted when you put it in a glass of water. The refractive index of a medium describes how much that medium can bend a ray of light. Consider the following setup where a light ray passes from air to a slab of glass. Air Glass Air Material 1 Material 2 Material n

Exercise for Submission: Part 1: Refraction is the binding of a light ray as it passes from one medium to another, for instance from air to water. This phenomenon is why your straw appears to be distorted when you put it in a glass of water. The refractive index of a medium describes how much that medium can bend a ray of light. Consider the following setup where a light ray passes from air to a slab of glass. Air Glass Air Material 1 Material 2 Material n

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Exercise for Submission: Part 1: Refraction is the binding of a light ray as it passes from one medium to another, for instance from air to water. This phenomenon is why your straw appears to be distorted when you put it in a glass of water. The refractive index of a medium describes how much that medium can bend a ray of light. Consider the following setup where a light ray passes from air to a slab of glass. Air Angle of incidence Glass Angle of refraction The angle of the light ray measured at the surface of the glass is called the 'angle of incidence' and the angle of the light ray inside the glass is called the 'angle of refraction'. Snell's law links these angles to the refractive indices as follows: n₁ sin 0₁ = n₂ sin 0₂ In the above equation, 0₁ and 0₂ are the angles of incidence and refraction respectively, and n₁, n₂ are the refractive indices of air and glass respectively. Now assume the following scenario: there are layers of materials, each with potentially different refractive indices, stacked side-by-side. Air ● ● Material 1 Assume that the user will supply the angle of incidence and the refractive indices of all the materials, derive the equation for the angle of refraction (in degrees) at the final layer (the right most in the diagram). You can: • ignore any reflection, loss of intensity, etc., Can assume that the layers are perfectly stacked (i.e., no gaps), ● The layers are large enough that the light will always reach the last layer, Assume that the refractive index of air is equal to 1, • Angles are in degrees, Use the first test case for your numerical part. Hints: Material 2 Material n You can start out by looking at one layer at a time, and considering the output of one layer as input to the next layer. O Does the final angle of refraction at the final layer depend on any of the middle layers?
Transcribed Image Text:Exercise for Submission: Part 1: Refraction is the binding of a light ray as it passes from one medium to another, for instance from air to water. This phenomenon is why your straw appears to be distorted when you put it in a glass of water. The refractive index of a medium describes how much that medium can bend a ray of light. Consider the following setup where a light ray passes from air to a slab of glass. Air Angle of incidence Glass Angle of refraction The angle of the light ray measured at the surface of the glass is called the 'angle of incidence' and the angle of the light ray inside the glass is called the 'angle of refraction'. Snell's law links these angles to the refractive indices as follows: n₁ sin 0₁ = n₂ sin 0₂ In the above equation, 0₁ and 0₂ are the angles of incidence and refraction respectively, and n₁, n₂ are the refractive indices of air and glass respectively. Now assume the following scenario: there are layers of materials, each with potentially different refractive indices, stacked side-by-side. Air ● ● Material 1 Assume that the user will supply the angle of incidence and the refractive indices of all the materials, derive the equation for the angle of refraction (in degrees) at the final layer (the right most in the diagram). You can: • ignore any reflection, loss of intensity, etc., Can assume that the layers are perfectly stacked (i.e., no gaps), ● The layers are large enough that the light will always reach the last layer, Assume that the refractive index of air is equal to 1, • Angles are in degrees, Use the first test case for your numerical part. Hints: Material 2 Material n You can start out by looking at one layer at a time, and considering the output of one layer as input to the next layer. O Does the final angle of refraction at the final layer depend on any of the middle layers?
Part 2: Note: A starter code is provided called A4_starter.py, use this as the template and fill out the necessary bits in the code to implement the required functionality. The code also contains comments that complement instructions in this document, so read both. Imagine that you are writing a Python program that will be used by a few geologica researchers. Each researcher has a set of unknown crystals and wants to determine what they are, and how they bend light. Each researcher has done a series of experiments to determine the refractive indices of a set of unknown materials. Unfortunately, their experiment does not produce exact values, but they are within +0.02 of known refractive indices of materials. They wish to know what the materials are, and what the angle of refraction would be if they stacked these materials together in various orders. You should create a Python program that takes in a set of comma separated values corresponding to the refractive indices of each layer in the stack. Your program must: 1. Determine the material corresponding to the given refractive index 2. Print out line-by-line the material name and the angle of refraction at that layer (2 decimal places). 3. Loop back until the user decides to quit. The following table lists some materials and their refractive indices: Material Diamond Sapphire Emerald Opal Pearl This table is given to you as a list-of-lists in the Python code. Each element of the outer list is a list of two items: the name and the refractive index. You must ONLY USE THE LIST-OF-LISTS to determine the most likely material corresponding to the user input. You will need to iterate over the list-of-lists and check for which of the materials has a refractive index that is within ±0.02 of a given layer. Assumptions: ● Refractive Index 2.42 1.78 1.58 1.45 1.52 User will always enter values that are reasonable. ● User may enter any number of values but will enter at least one value. Hints: Look at the .split() method covered in class to figure out how to separate the values. You can use a nested for loop to get the refractive index of each item, then decide if it is within +0.02 of known values. O Look at the abs() function covered in the class, can that be used here? Don't forget degrees to radians conversion, as necessary! Sample Input and Output (match exactly): Note: Contains 3 sets of inputs Enter the angle of incidence (in degrees):22.5 Enter the refractive indices as comma separated values:1.569,1.539,1.770,1.456,2.437 Layer 1 is made of Emerald. Angle of refraction is 14.12 degrees. Layer 2 is made of Pearl. Angle of refraction is 14.40 degrees. Layer 3 is made of Sapphire. Angle of refraction is 12.49 degrees. Layer 4 is made of Opal. Angle of refraction is 15.24 degrees. Layer 5 is made of Diamond. Angle of refraction is 9.03 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:y Enter the angle of incidence (in degrees):66.6 Enter the refractive indices as comma separated values:1.469,1.799,2.402,1.561 Layer 1 is made of Opal. Angle of refraction is 38.66 degrees. Layer 2 is made of Sapphire. Angle of refraction is 30.67 degrees. Layer 3 is made of Diamond. Angle of refraction is 22.46 degrees. Layer 4 is made of Emerald. Angle of refraction is 36.01 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:YES Enter the angle of incidence (in degrees):39 Enter the refractive indices as comma separated values:1.786,1.580 Layer 1 is made of Sapphire. Angle of refraction is 20.63 degrees. Layer 2 is made of Emerald. Angle of refraction is 23.47 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:no
Transcribed Image Text:Part 2: Note: A starter code is provided called A4_starter.py, use this as the template and fill out the necessary bits in the code to implement the required functionality. The code also contains comments that complement instructions in this document, so read both. Imagine that you are writing a Python program that will be used by a few geologica researchers. Each researcher has a set of unknown crystals and wants to determine what they are, and how they bend light. Each researcher has done a series of experiments to determine the refractive indices of a set of unknown materials. Unfortunately, their experiment does not produce exact values, but they are within +0.02 of known refractive indices of materials. They wish to know what the materials are, and what the angle of refraction would be if they stacked these materials together in various orders. You should create a Python program that takes in a set of comma separated values corresponding to the refractive indices of each layer in the stack. Your program must: 1. Determine the material corresponding to the given refractive index 2. Print out line-by-line the material name and the angle of refraction at that layer (2 decimal places). 3. Loop back until the user decides to quit. The following table lists some materials and their refractive indices: Material Diamond Sapphire Emerald Opal Pearl This table is given to you as a list-of-lists in the Python code. Each element of the outer list is a list of two items: the name and the refractive index. You must ONLY USE THE LIST-OF-LISTS to determine the most likely material corresponding to the user input. You will need to iterate over the list-of-lists and check for which of the materials has a refractive index that is within ±0.02 of a given layer. Assumptions: ● Refractive Index 2.42 1.78 1.58 1.45 1.52 User will always enter values that are reasonable. ● User may enter any number of values but will enter at least one value. Hints: Look at the .split() method covered in class to figure out how to separate the values. You can use a nested for loop to get the refractive index of each item, then decide if it is within +0.02 of known values. O Look at the abs() function covered in the class, can that be used here? Don't forget degrees to radians conversion, as necessary! Sample Input and Output (match exactly): Note: Contains 3 sets of inputs Enter the angle of incidence (in degrees):22.5 Enter the refractive indices as comma separated values:1.569,1.539,1.770,1.456,2.437 Layer 1 is made of Emerald. Angle of refraction is 14.12 degrees. Layer 2 is made of Pearl. Angle of refraction is 14.40 degrees. Layer 3 is made of Sapphire. Angle of refraction is 12.49 degrees. Layer 4 is made of Opal. Angle of refraction is 15.24 degrees. Layer 5 is made of Diamond. Angle of refraction is 9.03 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:y Enter the angle of incidence (in degrees):66.6 Enter the refractive indices as comma separated values:1.469,1.799,2.402,1.561 Layer 1 is made of Opal. Angle of refraction is 38.66 degrees. Layer 2 is made of Sapphire. Angle of refraction is 30.67 degrees. Layer 3 is made of Diamond. Angle of refraction is 22.46 degrees. Layer 4 is made of Emerald. Angle of refraction is 36.01 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:YES Enter the angle of incidence (in degrees):39 Enter the refractive indices as comma separated values:1.786,1.580 Layer 1 is made of Sapphire. Angle of refraction is 20.63 degrees. Layer 2 is made of Emerald. Angle of refraction is 23.47 degrees. Do you want to enter more values? Enter 'y' or 'yes' to continue, or anything else to quit:no
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