A holographic image appears to move as you change your viewing angle. Explain the kinematics involved in this phenomenon and calculate the apparent velocity of the moving image.
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When a holographic image appears to move as the viewing angle changes, it is due to the principle of parallax. Parallax is the apparent shift in the position of an object when viewed from different angles. It occurs because our eyes observe objects from two slightly different positions, providing us with slightly different perspectives.
To explain the kinematics involved in this phenomenon, let's consider a simple scenario. Suppose we have a holographic image of a ball floating in front of us. As we change our viewing angle, we can imagine two distinct positions from where we observe the ball.
Now, if we calculate the apparent velocity of the moving image, we need to determine the angular velocity at which we are changing our viewing angle.
Let's assume that the ball moves horizontally along the y-axis. As we change our viewing angle (θ), it implies that our line of sight also changes. This change in line of sight manifests as an angular displacement (Δθ) from one position to another.
The apparent velocity of the moving image can be calculated using the formula:
Apparent velocity = Distance traveled / Time taken
In this case, the distance traveled is the horizontal displacement of the ball, which can be approximated as the product of the radius of the ball and the angular displacement (Δθ). The time taken is the time it takes for us to change our viewing angle.
Thus, the formula becomes:
Apparent velocity = (Radius of ball) * (Δθ) / (Time taken)
The apparent velocity is typically measured in angular units per unit time (e.g., degrees per second or radians per second). The specific value would depend on the actual values of the radius of the ball, the angular displacement, and the time taken.
Therefore, by understanding the kinematics involved in the holographic image's motion and measuring the relevant parameters, we can calculate the apparent velocity of the moving image.
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