A person stands in front of a mirror at an amusement park. the person is left of a mirror. the mirror shows an upright image of the person that seems to be 4.0 meters behind the mirror. assume the image is 3.5 times the person's height.
a) is the image virtual or real ? explain.
b) what is the focal lenght of the mirror?
c) is the mirror concave or convex?
d) sketch the mirror on the right of the person . draw the image by ray racing as we did in class. ray trace by drawing two rays from the tip of the arrow, one parallel to the axis and the other intersecting the point where the mirror crosses the axis. label the object distance d0 and the image distance d1 .
Magnification M = di/do =3.5,
do = di/3.5 = 4/35.4 =1.14 m,
1/f =1/di + 1/do =
= 1/1.14 – ¼ = 0.625,
f =1.6 m.
This is the concave mirror.
To answer these questions, we need to apply the principles of mirror reflection and use the mirror equation. Here's how we can solve each part:
a) To determine if the image is virtual or real, we need to understand the behavior of light rays when they interact with mirrors. In this case, since the person is standing in front of the mirror and the mirror shows an upright image, we can conclude that the image is virtual. This is because the light rays do not converge at a point behind the mirror to form a real image, but rather they appear to diverge from a point behind the mirror, creating a virtual image.
b) The focal length of a mirror, denoted by 'f', is the distance between the mirror and its focal point. We can calculate the focal length using the mirror equation:
1/f = 1/do + 1/di
Given that the image appears to be 4.0 meters behind the mirror and the image is 3.5 times the person's height, we can assume the object distance (do) is the person's height. Thus, do = h.
Substituting the values, we have:
1/f = 1/h + 1/di
1/f = 1/h + 1/4.0 (since the image appears 4.0 meters behind the mirror)
Since we don't have the specific value for the person's height, we can't compute the exact focal length without additional information. However, we can use this equation to determine the focal length once we have the person's height.
c) To determine whether the mirror is concave or convex, we can analyze the behavior of the reflection. In this case, since the mirror shows an upright image, it implies that the mirror is concave. Concave mirrors produce upright, virtual images when the object is placed within the focal length of the mirror.
d) To sketch the mirror and image, you'll need to draw a simple diagram. Here are the steps to follow:
1. Draw a vertical line representing the mirror.
2. Place an arrow or stick figure on the left side of the line to represent the person.
3. Draw two rays emanating from the tip of the arrow:
- Draw one ray parallel to the axis (the vertical line).
- Draw another ray from the tip of the arrow, aiming towards the point where the mirror crosses the axis.
4. These two rays will be reflected by the mirror:
- The ray parallel to the axis will reflect back through the focal point.
- The ray heading towards the mirror's axis will reflect at the same angle it approached the mirror.
5. Extend these reflected rays behind the mirror to locate the virtual image formed.
6. Label the object distance as d0 (the distance between the arrow and the mirror), and label the image distance as d1 (the distance between the mirror and the location of the virtual image).
Remember, the exact positions of the rays and the image will depend on the person's height and the focal length, which we don't have in this question.