The image produced by a concave mirror is located 27 cm in front of the mirror. The focal length of the mirror is 13 cm. How far in front of the mirror is the object located?
To determine the distance of the object from the concave mirror, we can use the mirror formula:
```
1/f = 1/v - 1/u
```
Where:
f = focal length of the mirror (given as 13 cm)
v = image distance (given as 27 cm)
u = object distance (unknown)
Plugging in the given values, the formula becomes:
```
1/13 = 1/27 - 1/u
```
To find the value of u, let's solve for u using this equation.
To determine the distance of the object in front of the concave mirror, we can use the mirror equation:
1/f = 1/di + 1/do
where:
- f is the focal length of the mirror,
- di is the distance of the image from the mirror,
- do is the distance of the object from the mirror.
In this case, we are given:
- di = 27 cm
- f = 13 cm
Substituting these values into the mirror equation, we have:
1/13 = 1/27 + 1/do
To solve for do, we can move the terms around:
1/do = 1/13 - 1/27
To simplify the equation, we need to find a common denominator:
1/do = (27 - 13)/(13 * 27)
= 14/351
Now, we can take the reciprocal of both sides to solve for do:
do = 351/14
do = 25.0714 cm
Therefore, the object is located approximately 25.0714 cm in front of the concave mirror.
Try the old standby,
1/do + 1/do = 1/f = 1/13
Solve for image distance do.