A concave mirror is constructed so that a man at a distance of 19 cm from the mirror sees his image magnified 2.0 times. What is the radius of the curvature?
OK so I have tried to work this out and can't seem to find the answer. Here is what I got. Please let me know if you know what I am doing wrong?
m=2.0
do=19 cm
m=-di/do=hi/ho
m(do)=di
2.0(19)=di
di=-38
1/f=1/di+1/do
f=dodi/do-di
f=-12.7
f=r/2
r=-25
What am I doing wrong???
As I remember, M should be - for virtual inverted images. If he sees his own image, it must be virtual, Check that convention,please.
It seems like you made some mistakes in your calculations. Let's go through the problem step by step to find the correct answer.
Given information:
magnification (m) = 2.0
object distance (do) = 19 cm
We'll start by using the magnification equation for concave mirrors:
magnification (m) = -di/do, where di is the image distance and do is the object distance.
Plugging in the values:
2.0 = -di/19
To find the image distance (di), we can rearrange the equation:
di = -2.0 * 19
di = -38 cm
Next, we'll use the mirror formula to find the radius of curvature (r):
1/f = 1/di + 1/do, where f is the focal length.
Plugging in the values:
1/f = 1/-38 + 1/19
Simplifying the equation:
1/f = (-1/38) + (1/19)
1/f = (1 - 2)/38
1/f = -1/38
Taking the inverse of both sides:
f = -38
Since 1/f = 1/r, we can conclude that the radius of curvature (r) is also -38 cm.
Therefore, the correct answer for the radius of curvature is -38 cm, not -25 cm as you had calculated. Keep in mind that negative values for the radius indicate a concave mirror.