Concave mirrors can be used as for shaving or applying make up. The face must be inside the focus. You hold a concave mirror, with a focal length of 40 cm, about 30 cm from your face.
Where is your image located?
How much bigger than your face is the image?
To determine the location of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
where:
f is the focal length of the mirror,
v is the distance of the image from the mirror, and
u is the distance of the object from the mirror.
In this case, the focal length (f) of the concave mirror is given as 40 cm, and the object distance (u) is 30 cm. We need to calculate the image distance (v) and determine its location.
Substituting the given values into the formula:
1/40 = 1/v - 1/30
To solve for v, we can rearrange the equation:
1/v = 1/40 + 1/30
By finding the common denominator, we get:
1/v = (3 + 4) / (120)
1/v = 7 / 120
v = 120 / 7 ≈ 17.14 cm
Therefore, the image formed by the concave mirror is located at approximately 17.14 cm from the mirror.
To determine the size of the image compared to the object, we can use the magnification formula:
magnification (m) = -v/u
where:
m is the magnification,
v is the distance of the image from the mirror, and
u is the distance of the object from the mirror.
Substituting the given values:
m = -(17.14) / 30
m ≈ -0.571
The negative sign indicates that the image formed is virtual and upright compared to the object. The magnitude of the magnification tells us that the image is smaller than the object by a factor of approximately 0.571.
Therefore, the image formed by the concave mirror is located approximately 17.14 cm from the mirror, and it is about 0.571 times smaller than your face.