An object is placed 19.6 cm to the left of a diverging lens (f = -7.84 cm). A concave mirror (f = 11.2 cm) is placed 27.3 cm to the right of the lens
Find the final image distance, measured relative to the mirror (cm)
To find the final image distance relative to the mirror, we can use the lens mirror formula and apply the sign conventions.
The lens mirror formula is given by:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens (given as -7.84 cm, indicating a diverging lens)
- do is the object distance from the lens (given as 19.6 cm)
- di is the image distance from the lens (unknown in this case)
To solve for di, we need to rearrange the formula:
1/di = 1/f - 1/do
Now, let's substitute the given values:
1/di = 1/-7.84 - 1/19.6
Simplifying further, we get:
1/di = -0.1276 + 0.051
1/di = -0.0766
Taking the reciprocal on both sides, we get:
di = -1 / (-0.0766)
di = 13.06 cm
The image formed by the lens is located 13.06 cm to the right of the lens.
Now, let's consider the concave mirror. The object distance for the mirror is equal to the image distance from the lens. Therefore, the object distance for the mirror is 13.06 cm.
To find the final image distance relative to the mirror, we can use the mirror formula:
1/f = 1/do + 1/di
Where:
- f is the focal length of the mirror (given as 11.2 cm)
- do is the object distance from the mirror (given as 13.06 cm)
- di is the image distance from the mirror (unknown)
To solve for di, we rearrange the formula:
1/di = 1/f - 1/do
Substituting the values:
1/di = 1/11.2 - 1/13.06
Simplifying further, we get:
1/di = 0.0893 - 0.0766
1/di = 0.0127
Taking the reciprocal on both sides, we get:
di = 1 / 0.0127
di = 78.74 cm
Therefore, the final image distance, measured relative to the mirror, is 78.74 cm.