Find the final image of object after all refractions and reflections. Please solve the example stepwise.

To find the final image of an object after all refractions and reflections, we can break down the process into clear steps. Let’s consider a practical example involving a lens and a mirror. This will help illustrate how to determine the final image position. We’ll use a convex lens and a flat mirror for this scenario.

Step 1: Understanding the Setup

Imagine we have an object placed in front of a convex lens, which is then followed by a flat mirror. For simplicity, let’s say the object is 10 cm away from the lens, and the focal length of the lens is 5 cm. The distance from the lens to the mirror is 15 cm.

Step 2: Finding the Image Formed by the Lens

To find the image formed by the lens, we can use the lens formula:

• 1/f = 1/v - 1/u

Where:

• f = focal length of the lens
• v = image distance from the lens
• u = object distance from the lens (taken as negative in lens formula)

Substituting the values:

• f = 5 cm
• u = -10 cm

Now, substituting these into the lens formula:

• 1/5 = 1/v - 1/(-10)

This simplifies to:

• 1/5 = 1/v + 1/10

To solve for v, we first find a common denominator:

• 1/5 - 1/10 = 2/10 - 1/10 = 1/10

Thus, we have:

• 1/v = 1/10

Therefore, the image distance v is:

• v = 10 cm

This means the image formed by the lens is located 10 cm on the opposite side of the lens from the object.

Step 3: Position of the Image Relative to the Mirror

Next, we need to determine the position of this image relative to the mirror. Since the lens is 15 cm away from the mirror, we can find the distance from the mirror:

• Distance from lens to mirror = 15 cm
• Image distance from lens = 10 cm

Thus, the distance from the image to the mirror is:

• 15 cm - 10 cm = 5 cm

This means the image formed by the lens is 5 cm in front of the mirror.

Step 4: Finding the Image Formed by the Mirror

When light reflects off a flat mirror, the image distance is equal to the object distance from the mirror. Therefore, the image formed by the mirror will be:

• Image distance from the mirror = 5 cm (behind the mirror)

Since the image is virtual and located behind the mirror, we can say that the final image is 5 cm behind the mirror.

Final Summary

In this example, we started with an object 10 cm in front of a convex lens. The lens produced an image 10 cm on the opposite side, which was 5 cm in front of a flat mirror. The mirror then created a virtual image 5 cm behind it. Thus, the final image is located 5 cm behind the mirror, resulting from the combined effects of refraction through the lens and reflection from the mirror.