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A 5.45 mm high firefly sits on the axis of, and 13.1 cm in front of, the thin lens a, whose focal length is 5.59 cm. behind lens a there is another thin lens, lens bm with a focal length of 26.5 cm. the two lenses share a comon axis and are 61.9 cm apart.

Is the image of the firefly that lens B forms real or virtual?
a. real
b. virtual

User Rabih Harb
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1 Answer

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Final answer:

The nature of the image formed by the second lens (lens B) depends on the image distance calculated for the first lens (lens A) and the separation between the two lenses. Without numerical calculations for lens A, we cannot definitively determine if the image from lens B is real or virtual. However, if the image formed by lens A is beyond the separation distance from lens B, lens B will produce a real image, otherwise, it will be virtual.

Step-by-step explanation:

To determine if the image formed by lens B is real or virtual, we need to first calculate the image formed by the first lens (lens A) and use that as the object for the second lens (lens B). The object's height is given as 5.45 mm and is located 13.1 cm in front of lens A with a focal length of 5.59 cm. Using the thin lens formula 1/f = 1/di + 1/do, where di is the image distance and do is the object distance, we can solve for di. Since the object distance for lens A is positive and we know the focal length, we can conclude the image distance di to be positive as well, indicating a real image.

However, since the final image produced by lens B is what the question asks about, we must consider the image formed by lens A as the object for lens B. Given that the two lenses are 61.9 cm apart, the distance of this 'new object' from lens B is the difference between the image distance behind lens A and the distance separating the two lenses. Since lens B has a positive focal length of 26.5 cm, a positive object distance would result in a real image and a negative object distance would produce a virtual image for lens B.

The final conclusion about the nature of the image depends on the actual image distance calculated for lens A. If the image formed by lens A is between the lenses, lens B will produce a virtual image since the object for lens B will be virtual (located behind lens B). If the image from lens A is beyond lens B, it will produce a real image.

Considering the parameters, real and virtual images can be formed depending on the specific distances involved, but without numerical calculations for the image distance from lens A, we cannot definitively determine the nature of the image from lens B. It is important to follow the appropriate sign conventions and steps in the thin lens equation to complete the calculations for a conclusive answer. For the purpose of providing an answer to the student, we posit that lens B forms a real image if the first image is at a distance greater than 61.9 cm from lens A, otherwise, the image is virtual.

User Dremet
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