A 1.5 m tall man stands 2 m in front of a flat wall mirror. Please find: image distance and height of image
I have the formulas but i don't know how to solve this without the focal point or a radius...pls help!!!!!!!
image distance 2metres behind mirror
height is 1.5metres
for plane mirror focal length is infinty
so 1/f=1/v + 1/u reduces to
v= -u
v= -(-2)=2
magnification = -v/u=1
To solve this problem, you can use the mirror equation, which relates the object distance (the distance between the object and mirror), image distance (the distance between the image and mirror), focal length (f), and the height of the object (h).
The mirror equation is: 1/f = 1/di + 1/do
Where:
- f is the focal length of the mirror
- di is the image distance
- do is the object distance
In this case, we have the object distance (do) as 2 m in front of the mirror. As this problem mentions a flat wall mirror, we can assume that the focal length is infinite (since a flat mirror doesn't have a specific focal point).
With an infinite focal length, the mirror equation simplifies to: di = -do
So, the image distance (di) would be -2 m.
Now, we can calculate the height of the image. We'll use the magnification equation, which relates the height of the image (hi) and the height of the object (ho) to the magnification (m) and object distance (do):
m = -di/do = hi/ho
In this case, the magnification (m) is -1, since the image is formed upright and equidistant from the mirror. Therefore:
-1 = hi/h0
Since the height of the object (ho) is given as 1.5 m, we can solve for the height of the image (hi):
-1 = hi/1.5
Multiplying both sides by 1.5, we get:
-1.5 = hi
So, the height of the image (hi) is -1.5 m.
However, since the negative sign indicates that the image is inverted, we take the absolute value of the height, so the actual height of the image is 1.5 m.
To summarize:
- The image distance (di) is -2 m.
- The height of the image (hi) is 1.5 m.