A convex mirror (f1 = −6.30 cm) and a concave mirror (f2 = 9.50 cm) are facing each other and are separated by a distance of 24.0 cm. An object is placed between the mirrors and is 12 cm from each mirror. Consider the light from the object that reflects first from the convex mirror and then from the concave mirror. What is the distance of the image (di2) produced by the concave mirror?.

To find the distance of the image (di2) produced by the concave mirror, we can use the mirror formula:

1/f = 1/do + 1/di,

where f is the focal length, do is the object distance, and di is the image distance.

Given:
f1 (convex mirror) = -6.30 cm,
f2 (concave mirror) = 9.50 cm,
Separation between mirrors = 24.0 cm,
Object distance from both mirrors (do) = 12 cm.

First, we need to find the image distance (di1) produced by the convex mirror using the mirror formula:

1/f1 = 1/do + 1/di1.

Substituting the values:
1/-6.30 = 1/12 + 1/di1.

Solving this equation, we find the image distance (di1) produced by the convex mirror.

Next, we need to find the object distance (do2) for the concave mirror. Since the light reflects from the convex mirror and then reaches the concave mirror, the object distance for the second mirror will be the sum of the image distance produced by the convex mirror (di1) and the separation between the mirrors (24.0 cm). Therefore:

do2 = di1 + 24.0.

Now we can find the image distance (di2) produced by the concave mirror using the mirror formula:

1/f2 = 1/do2 + 1/di2.

Substituting the values:
1/9.50 = 1/(di1 + 24.0) + 1/di2.

We already know the value of di1, so we can solve this equation to find the image distance (di2) produced by the concave mirror.

Once we find di2, we will have the desired distance of the image produced by the concave mirror.