A lady applies makeup using a concave mirror with a focal length of 10 cm. At a distance of 6 cm from the mirror, how large does her 4 cm wide eye appear? Solve mathematically
To solve this mathematically, we can use the mirror formula:
1/f = 1/u + 1/v
Where:
- f is the focal length of the mirror,
- u is the object distance (distance of the eye from the mirror), and
- v is the image distance (distance of the image from the mirror).
In this case, the focal length (f) of the concave mirror is given as 10 cm, and the object distance (u) is 6 cm.
Substituting the known values into the mirror formula:
1/10 = 1/6 + 1/v
Simplifying the equation:
1/10 - 1/6 = 1/v
Multiplying through by the common denominator (60v):
6v - 10v = 60
-4v = 60
Dividing both sides by -4:
v = -60/4
v = -15
Since the value of v is negative, it means that the image formed is virtual (upright). The magnitude of the image distance (-15) tells us the distance of the image from the mirror.
Now, to determine the size of the image, we can use the magnification formula:
Magnification (m) = -v/u
Substituting the values of v = -15 and u = 6 into the formula:
m = -(-15)/6
m = 2.5
The magnification tells us that the image is enlarged by a factor of 2.5.
Since the eye is 4 cm wide, the width of the image can be determined by multiplying the actual width of the eye by the magnification factor:
Image width = Actual width × Magnification
Image width = 4 cm × 2.5
Image width = 10 cm
Therefore, the eye appears to be 10 cm wide when viewed through the concave mirror.