Periscope Design and Mirror Reflection
Published:
PHYSICS
Item 1
In 1979 a military coup of the NRA started in Luwero. Many of the soldiers were killed during spying of their enemies especially in hilly and mountainous areas. The bag of the chief commander, there was two plane mirrors and a plastic rectangular vessel.
Task
Using the knowledge of physics.
a) Help the NRA army by designing an instrument which can help them in spying without being killed.
b) If the angle of inclination of the mirrors was (i) $90^{\circ}$, (ii) $60^{\circ}$, $30^{\circ}$ and $20^{\circ}$. Draw a summary table for the number of images formed.
Animated Video Solution
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Step by Step Written Solution
Hi Mabirizi, let's solve this together. We are asked to design a spying instrument using two plane mirrors and a rectangular vessel, and then calculate the number of images formed at different angles of inclination.
Problem Overview\n- Part a: Design a spying instrument (Periscope).\n- Part b: Calculate the number of images formed at inclination angles $90^\circ, 60^\circ, 30^\circ,$ and $20^\circ$.
Let's begin with Part a. To spy from behind obstacles or hills without being seen, we can construct a periscope. A periscope uses a long rectangular outer casing with two plane mirrors mounted parallel to each other and inclined at an angle of forty-five degrees to the walls of the tube.
Part a) Designing a Periscope
Let's trace how light rays travel through this device. Light from the object enters the top window horizontally, hits the first mirror at forty-five degrees, and is reflected ninety degrees downward.
Then, the downward light ray travels through the tube to hit the second mirror, which reflects it ninety degrees horizontally again into the observer's eye, safely located behind cover.
Now let's move on to Part b. We need to find the number of images formed by two plane mirrors inclined at an angle theta. The formula for the number of images, n, is given by three hundred and sixty degrees divided by theta minus one.
Part b) Number of Images Formed
Let's first calculate for an inclination angle of ninety degrees. Plugging ninety degrees for theta into our formula gives us three hundred and sixty divided by ninety minus one.
Case 1: $\theta = 90^\circ$
Three hundred and sixty divided by ninety is four, and subtracting one gives us exactly three images.
Next, let's calculate for sixty degrees. Substituting sixty degrees into the formula gives us three hundred and sixty divided by sixty minus one.
Case 2: $\theta = 60^\circ$
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