Question

A diverging lens (f₁ =−10.0 cm) is located 45.0 cm to the left of a converging lens (f₂ =21.0 cm). A 3.5−cm⋅-tall object stands to the left of the diverging lens, exoctly at its focal point. Determine the distance of the final image relative to the converging lens (including proper algebraic sign).

Answer 1

To find the distance of the final image relative to the converging lens, analyze the system of lenses and use the thin lens equation. The object placed at the focal point of the diverging lens forms an image at infinity. The image acts as the object for the converging lens, and by using the thin lens equation, the image distance can be calculated.

Step-by-step explanation:

To determine the distance of the final image relative to the converging lens, we need to analyze the system of lenses. Let's first find the position of the image formed by the diverging lens. Since the object is placed at the focal point of the diverging lens, the image formed by this lens will be at infinity, resulting in parallel rays.

Now, these parallel rays act as the object for the converging lens. We can use the thin lens equation for the converging lens:

1/f = 1/di - 1/do

where f is the focal length of the converging lens, di is the image distance, and do is the object distance. In this case, the object distance is equal to the focal length of the diverging lens.

By substituting the values into the equation, we can solve for di. Once we obtain the image distance, we can determine the distance of the final image relative to the converging lens.