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ladessa
8 days ago
11

Two thin lenses with a focal length of magnitude 12.0cm, the first diverging and the second converging, are located 9.00cm apart

. An object 2.50mm tall is placed 20.0cm to the left of the first (diverging) lens. Note that focal length of diverging lens is a negative number while focal length of converging lens would be positive.
(a) Draw a figure showing both lenses and use principal rays to find approximate position of the image formed by the first lens.
(b) Calculate how far from this first lens is the first image formed.
(c) Calculate how far from this first lens is the final image formed.
(d) What is the height of the final image?
(e) Is it erect or inverted?
Physics
1 answer:
kicyunya [3.2K]8 days ago
6 0
b ) The first lens is a concave lens with a focal length of f₁ = - 12 cm and an object distance of u = - 20 cm. Using the lens formula, 1 / v - 1 / u = 1 / f, we get 1 / v + 1 / 20 = -1 / 12. This leads to 1 / v = - 1 / 20 - 1 / 12, which simplifies to 1 / v = -0.05 - 0.08333, yielding v = -7.5 cm. Consequently, the first image is formed before the first lens, near the object side, which becomes the object for the second lens with a distance of 16.5 cm from the second lens. c ) For the second lens, object distance is u = -16.5 cm, and focal length f₂ = + 12 cm (convex lens). Using the lens formula leads to 1 / v + 1 / 16.5 = 1 / 12, and this results in 1 / v = 1 / 12 - 1 / 16.5, which simplifies to 1 / v = 0.08333 - 0.0606. Finally, we find v = 44 cm (approximately). This image will be formed on the other side of the convex lens, which is 53 cm from the first lens. Magnification by the first lens is v / u = -7.5 / -20 = 0.375. For the second lens, it is v / u = 44 / - 16.5 = -2.67. d ) The total magnification becomes 0.375 x - 2.67 = - 1.00125. The height of the final image is then calculated as 2.50 mm x 1.00125 = 2.503 mm. e ) The final image will be inverted compared to the object since the total magnification is negative.
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The full articulation of the query is

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Explanation:

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When we add these equations, one A2B cancels out with one A2B from reaction 2, thus, we have:

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