1. A concave mirror forms a real image at 25cm from he mirror surface along the principal axis. If the corresponding object is at a 10cm distance, what is the mirror's focal length?
2. A woman looking in a makeup mirror sees her face at twice its actual size and right-side up. If she is 28cm from the mirror, what is its focal length?
1. Learn the formula
1/Do + 1/Di = 1/f
Then use it.
In this case Do = object distance = 10 cm
Di = image distance = 25 cm.
Solve for f
2. Do = 28
Di = -56
The magnification is 2 = |Di/Do|
Di is negative for an upright image.
Solve for f
Use the same equation as part 1 to solve for f.
1. 14.2
1. Given:
- Image distance (d_i) = 25 cm
- Object distance (d_o) = -10 cm (Negative sign indicates that object distance is on the same side as the object)
To find the focal length of the concave mirror, we can use the mirror formula:
1/f = 1/do + 1/di
Substituting the given values:
1/f = 1/-10 + 1/25
1/f = -0.1 + 0.04
1/f = -0.06
Now, we can take the reciprocal on both sides to find the focal length:
f = -1 / (-0.06)
f ≈ 16.67 cm
Therefore, the focal length of the concave mirror is approximately 16.67 cm.
2. Given:
- Magnification (m) = 2 (positive value indicates an upright image)
- Object distance (d_o) = 28 cm
To find the focal length of the mirror, we can use the magnification formula:
m = -di / do
Rearranging the formula, we get:
di = -m * do
Substituting the given values:
di = -(2) * 28
di = -56 cm
Now, we can use the mirror formula to find the focal length:
1/f = 1/do + 1/di
Substituting the values:
1/f = 1/28 + 1/-56
1/f = 0.0357 - 0.0179
1/f = 0.0178
Taking the reciprocal on both sides:
f ≈ 56 cm
Therefore, the focal length of the mirror is approximately 56 cm.
To find the focal length of 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 image distance from the mirror surface, and
u is the object distance from the mirror surface.
For question 1:
Given that the real image is formed at a distance of 25 cm from the mirror surface and the object distance is 10 cm.
Plugging in the values into the mirror formula:
1/f = 1/25 - 1/10
Simplifying:
1/f = 4/100 - 10/100
1/f = -6/100
1/f = -1/16
Taking the reciprocal of both sides:
f = -16 cm
The focal length of the concave mirror is -16 cm (negative sign indicates concave mirror).
For question 2:
Given that the woman sees her face at twice its actual size and right-side up, we can determine that the position of the image is at 2 times the object distance.
Plugging in the values into the mirror formula:
1/f = 1/v - 1/u
1/f = 1/(2u) - 1/u
Simplifying:
1/f = 1/u - 1/(2u)
1/f = 1/(2u)
Given that the object distance is 28 cm, we substitute the value into the equation:
1/f = 1/(2 * 28)
1/f = 1/56
Taking the reciprocal of both sides:
f = 56 cm
The focal length of the makeup mirror is 56 cm.