Consider a concave mirror with a focal length
of 14.04 cm.
b) Find the image distance when the object
distance is 7.02 cm
c) Find the magnification of the image for
part b
Giving me the formulas is just fine
The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f):
1/f=1/d(o)+1/d(i)
The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).
M=h(i)/h(o)= - d(i)/d(o)
To find the image distance (b), when the object distance (u) is given, we can use the mirror formula for concave mirrors:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror,
- v is the image distance, and
- u is the object distance.
To find the image distance (v) when the object distance (u) is 7.02 cm, we can substitute the values into the formula:
1/14.04 = 1/v - 1/7.02
To simplify this equation, we can find the common denominator:
1/14.04 = (7.02 - v)/7.02
Now, cross-multiply and simplify:
7.02 = 14.04 - v
v = 14.04 - 7.02
v = 7.02 cm
So, the image distance is also 7.02 cm.
Moving on to the magnification (m), we can use the magnification formula:
m = -v/u
Where:
- m is the magnification,
- v is the image distance, and
- u is the object distance.
Using the values from part b, we can substitute them into the formula:
m = -7.02/7.02
m = -1
Therefore, the magnification of the image for part b is -1.