a periscope is an optical instrument made of two plane mirrors inclined at an angle 45 with respect to the axis of the tube. an observer places her eye at point O. draw the path of a ray light issued from A. determine the position and the nature of the image of A given by two mirror system.
identical
Trace ray from the top of A and then another from the bottom of A
To draw the path of the light ray from point A, we need to understand the principles of reflection for a periscope. A periscope consists of two plane mirrors inclined at an angle of 45 degrees with respect to the axis of the tube. Let's visualize the arrangement:
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A O
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In this diagram, A represents the source of light, and O represents the observer's eye position.
Now, let's draw the path of the light ray. According to the law of reflection, the angle of incidence is equal to the angle of reflection, and the incident ray, reflected ray, and the normal at the point of incidence all lie in the same plane.
1. Draw a line from point A, inclined at a 45-degree angle with the mirror. This line represents the incident ray.
2. Using a ruler, measure the angle of incidence (which should be 45 degrees) and construct a line on the opposite side of the mirror inclined at the same angle. This line represents the reflected ray.
3. Since the observer places her eye at point O, draw a line from the point of incidence to point O. This line represents the path taken by the light ray to reach the observer's eye.
Now, let's determine the position and nature of the image formed by this two-mirror system.
The image formed by a periscope is a virtual image. It is located at a point where the reflected rays from each mirror converge or appear to diverge. In this case, the image of point A will be formed by the merging of the reflected rays.
To determine the position of the image, we can extend the reflected rays until they intersect. The point of intersection is where the image of point A will appear.
Given that the mirrors are inclined at a 45-degree angle, the reflected rays will converge or diverge at a distant point based on the observer's eye at point O. The actual position of the image will vary depending on the distance between the observer and the periscope's mirrors.
The exact formula to calculate the position of the image can be determined using geometry and trigonometry, considering the angles and distances involved.