An object is placed 27.0 cm to the left of a lens of focal length 17.0 cm.39.0 cm to the right of this lens is a plane mirror.Where does the final image form?
A)6.9 cm to the right of the mirror
B)6.9 cm to the left of the mirror
C)32.1 cm to the left of the lens
D)45.9 cm to the left of the lens
E)28.6 cm to the left of the mirror

Question

Quizplus · Accepted Answer

First, we need to find the position of the image formed by the lens alone. We can use the lens formula:
1/f = 1/do + 1/di
where f is the focal length, do is the object distance, and di is the image distance.
Substituting the given values, we get:
1/17 = 1/27 + 1/di
Solving for di, we get:
di = 45.9 cm
So, the image formed by the lens is 45.9 cm to the left of the lens.
Now, this image acts as the virtual object for the plane mirror. The distance between the image and the mirror is 39 cm, so the distance between the virtual object and the mirror is also 39 cm.
Using the mirror formula:
1/do' + 1/di' = 1/f'
where f' is the focal length of the mirror, which is infinity for a plane mirror, and do' and di' are the object and image distances measured from the mirror.
Since the object is at infinity, we can simplify the formula to:
1/di' = 1/f'
Solving for di', we get:
di' = -39 cm
The negative sign indicates that the image is formed behind the mirror, which is expected for a plane mirror.
So, the final image is 39 cm behind the mirror, which is equivalent to 6.9 cm to the left of the mirror. Therefore, the answer is B.

An Object Is Placed 27