Question

Standing 2.2 m in front of a small vertical mirror, you see the reflection of your belt buckle, which is 0.70 m below your eyes.A) What is the vertical location of the mirror relative to the level of your eyes?B) What angle do your eyes make with the horizontal when you look at the buckle?C) If you now move backward until you are 6.0 m from the mirror, will you still see the buckle, or will you see a point on your body that is above or below the buckle? Explain.

Answer 1

The vertical location of the mirror is the same as the distance of the eyes to the belt buckle, or 0.70 m. The angle of the eyes with the horizontal can be found using trigonometry with arctan(0.70/2.2). When moving back to 6.0 m, the ability to see the buckle depends on the mirror's height and the new angle of line of sight.

Step-by-step explanation:

To solve this Physics problem related to the Law of Reflection, we need to apply the principles of ray tracing and geometry.

Part A: Vertical Location of the Mirror

The vertical location of the mirror relative to the level of the eyes is the distance from the eyes to the belt buckle because the distance in front of the mirror will be the same as the distance behind the mirror where the image of the buckle appears. Since the buckle is 0.70 m below the eyes, the mirror must be at least 0.70 m tall to reflect the image of the buckle back to the eyes.

Part B: Angle with the Horizontal

To find the angle your eyes make with the horizontal when looking at the buckle, we use trigonometry. Let θ be the angle, then tan(θ) = opposite/adjacent which is 0.70/2.2. Calculate θ = arctan(0.70/2.2).

Part C: Visibility of Buckle from a Distance of 6.0 m

If you now move backwards to 6.0 m, the line of sight angle to the belt buckle changes. Whether you can still see the buckle depends on the new angle and if the mirror is tall enough to reflect the image of the buckle to your eyes at that distance. If the mirror's height hasn't changed, the path of the reflected ray will be at a different angle, potentially showing a point on your body above or below the buckle, depending on the height of the mirror.

Answer 2

A) The vertical location of the mirror relative to the level of your eyes is 2.25 m. B) The angle your eyes make with the horizontal when you look at the buckle is 18.4 degrees. C) If you move backward until you are 6.0 m from the mirror, you will not be able to see the buckle, but a point on your body below it.

Step-by-step explanation:

A) The vertical location of the mirror relative to the level of your eyes is equal to the height of the mirror plus the distance between your eyes and the top of your head. In this case, the mirror's vertical location is 0.7 m + (2.2 m - 1.65 m) = 2.25 m.

B) The angle your eyes make with the horizontal when you look at the buckle can be found using simple trigonometry. The vertical distance from your eyes to the buckle is 0.7 m, and the horizontal distance is 2.2 m. Therefore, the angle can be calculated as arctan(0.7 m / 2.2 m) = 18.4 degrees.

C) If you move backward until you are 6.0 m from the mirror, the vertical location of the mirror will still be 2.25 m. Therefore, you will not be able to see the buckle anymore since it is below the mirror's vertical location. You will see a point on your body that is below the buckle.