An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers (n = 3.50). 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 0.50 ns to process a request. If the information has to be obtained from memory in 2.00 ns, what is the maximum distance the memory unit can be from the central processing unit?

d = 6.43 cm

Explanation:

Given:

- Speed resistance coefficient in silicon n = 3.50

- Memory takes processing time t_p = 0.50 ns

- Information is to be obtained within T = 2.0 ns

Find:

- What is the maximum distance the memory unit can be from the central processing unit?

Solution:

- The amount of time taken for information pulse to travel to memory unit:

t_m = T - t_p

t_m = 2.0 - 0.5 = 1.5 ns

- We will use a basic relationship for distance traveled with respect to speed of light and time:

d = V*t_m

- Where speed of light in silicon medium is given by:

V = c / n

- Hence, d = c*t_m / n

-Evaluate: d = 3*10^8*1.5*10^-9 / 3.50

d = 0.129 m 12.9 cm

- The above is the distance for pulse going to and fro the memory and central unit. So the distance between the two is actually d / 2 = 6.43 cm