A concave mirror has a focal length of 37 cm.
Determine the object position for which the resulting image is upright and four times the size of the object.
Answer in units of cm
30cm
30
To determine the object position for which the resulting image is upright and four times the size of the object, we can use the mirror equation:
1/f = 1/do + 1/di
Where:
- f is the focal length
- do is the object distance (distance of the object from the mirror)
- di is the image distance (distance of the image from the mirror)
Given:
f = 37 cm
Since the question states that the resulting image is upright and four times the size of the object, we can infer that the image distance (di) will be positive, and the magnification (m) will be +4.
The magnification (m) is given by the formula:
m = -di/do
Substituting the given values, we have:
4 = -di/do
Rearranging the equation, we get:
do = -di/4
Now, substitute the value of do into the mirror equation:
1/f = 1/do + 1/di
1/37 = 1/(-di/4) + 1/di
To solve for di, we can use algebraic manipulation:
1/37 = 4/di - 1/4di
Getting a common denominator:
1/37 = (4 - 1/4) / di
Simplifying:
1/37 = (15/4) / di
Next, cross-multiply:
4 * 1 = 37 * 15 / di
4 = 555 / di
Multiplying both sides by di:
4di = 555
Finally, solving for di:
di = 555/4
Therefore, the image distance is di = 138.75 cm.
Since the image distance (di) is positive, it means the image is real and located on the same side as the object. Thus, the object position (do) is -di/4:
do = -138.75 / 4
do = -34.69 cm
So, the object position for which the resulting image is upright and four times the size of the object is approximately -34.69 cm.