A man 1.5meter tall stands in front of a concave mirror whose radius is 30cm. Find the position of the man that will lead to his image on the screen 20 cm. from the mirror. How big is the man's image?
The focal length of the mirror is R/2 = 15 cm.
You must by now be familiar with the equation
1/do + 1/di = 1/f
which in your case becomes
1/do + 1/20 = 1/15
Solve for do (the object distance). The magnification will be di/do.
Multiply that by 1.5 meters for the image size
To find the position of the man that will lead to his image on the screen, we can make use of the mirror equation:
1/f = 1/v - 1/u
where,
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
We can determine the focal length (f) of the mirror using the mirror's radius (R):
f = R/2
Plugging in the values, we get:
f = 30 cm รท 2 = 15 cm
Now, let's substitute the given values into the mirror equation and solve for u:
1/15 = 1/20 - 1/u
Rearranging the equation, we have:
1/u = 1/15 - 1/20
Combining the fractions, we get:
1/u = (20 - 15) / (20 * 15)
= 5 / 300
= 1/60
To find u, we take the reciprocal of both sides:
u = 60 cm
Therefore, the position of the man from the mirror is 60 cm.
To determine the size of the man's image, we can use the magnification formula:
magnification (m) = -v/u
Here, the negative sign indicates that the image is inverted.
Substituting the values, we get:
m = -v/u
m = -20 cm / 60 cm
m = -1/3
The magnification is -1/3. This means that the image is one-third the size of the object and is inverted.