An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers. To acquire data from memory, the central processing unit sends a light-pulse request to the memory unit. The memory unit processes the request, then sends a data pulse back to the central processing unit. The memory unit takes to process a request. If the information has to be obtained from memory in , what is the maximum distance the memory unit can be from the central processing unit?
The maximum distance between the memory unit and the central processing unit is .
We have been given that an advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers. The memory unit takes to process a request. The time taken by the memory unit to deliver the information back to the central processing unit is .
We need to find the the maximum distance between the memory unit and the central processing unit.
The refractive index of silicon is .
The speed of light through the silicon fibers can be calculated by :
, where is speed of light in silicon fibers, is speed of light in vacuum, is the refractive index of silicon.
Substituting and , we get:
On simplifying, we get:
The time taken by the infrared light to travel to the memory unit from the central processing unit is
We can find the total distance travelled by the infrared light by the following formula:
Substituting the values of and , we get:
The distance between the central processing unit and the memory unit is half of the total distance travelled:
Substituting the value of , we get:
Shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles and in the two media. Suppose that you did not know Snell’s law.
A. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n1 and n2
B. The time depends on x. There’s one value of x for which the light travels from A to B in the shortest possible time. We’ll call it . Write an expression (but don’t try to solve it!) from which could be found.
C. Now, by using the geometry of the figure, derive Snell’s law from your answer to part b.
You’ve proven that Snell’s law is equivalent to the statement that “light traveling between two points follows the path that requires the shortest time.” This interesting way of thinking about refraction is called Fermat’s principle.
Suppose you have two pinhole cameras. The first has a small round hole in the front. The second is identical except it has a square hole of the same area as the round hole in the first camera. Would the pictures taken by these two cameras, under the same conditions, be different in any obvious way? Explain.
A -tall object is in front of a converging lens that has a focal length.
Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram. Calculate the image position and height. Compare with your ray-tracing answers in part .
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