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Chapter 24: Problem 39

The wing of an insect is \(1.0 \mathrm{mm}\) long. When viewed through a microscope, the image is \(1.0 \mathrm{m}\) long and is located \(5.0 \mathrm{m}\) away. Determine the angular magnification.

Short Answer

Expert verified
Answer: The angular magnification of the microscope is 50.

Step by step solution

01

Calculate the angle subtended by the insect wing when viewed with the naked eye

To calculate the angle subtended by the wing in the naked eye, we assume standard viewing distance of 25 cm or 0.25 m. Then we use the small angle approximation formula: tan θ ≈ θ = object size (height) / distance, where θ is the angle subtended by the object. θ_naked_eye = (1.0 mm) / (0.25 m) We need to convert the object size in mm to meters: 1.0 mm = 0.001 m. θ_naked_eye = (0.001 m) / (0.25 m)
02

Calculate the angle subtended by the insect wing when viewed through the microscope

This time, we're given the size of the image when viewed through the microscope (1.0 m), and the distance of the image from the eye (5.0 m). Using the small angle approximation formula again, we can calculate the angle subtended by the image formed through the microscope. θ_microscope = object size (height) / distance θ_microscope = (1.0 m) / (5.0 m)
03

Calculate the angular magnification

The angular magnification is the ratio of the angle subtended by the object when viewed through a microscope to the angle subtended by the object when viewed with the naked eye. M = θ_microscope / θ_naked_eye M = (1.0 m / 5.0 m) / (0.001 m / 0.25 m)
04

End: Final Answer

With all the necessary calculations, we can now determine the angular magnification of the microscope. M = (1.0/5.0)/(0.001/0.25) = 0.2/0.004 = 50. So the angular magnification of the microscope is 50.

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Most popular questions from this chapter

An object is located at \(x=0 .\) At \(x=2.50 \mathrm{cm}\) is a converging lens with a focal length of \(2.00 \mathrm{cm},\) at \(x=16.5 \mathrm{cm}\) is an unknown lens, and at \(x=19.8 \mathrm{cm}\) is another converging lens with focal length \(4.00 \mathrm{cm} .\) An upright image is formed at $x=39.8 \mathrm{cm} .$ For each lens, the object distance exceeds the focal length. The magnification of the system is \(6.84 .\) (a) Is the unknown lens diverging or converging? (b) What is the focal length of the unknown lens? (c) Draw a ray diagram to confirm your answer.
A cub scout makes a simple microscope by placing two converging lenses of +18 D at opposite ends of a \(28-\mathrm{cm}^{-}\) long tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?
An astronomical telescope provides an angular magnification of 12. The two converging lenses are \(66 \mathrm{cm}\) apart. Find the focal length of each of the lenses.
A photographer wishes to take a photograph of the Eiffel Tower $(300 \mathrm{m}\( tall ) from across the Seine River, a distance of \)300 \mathrm{m}$ from the tower. What focal length lens should she use to get an image that is 20 mm high on the film?
A camera with a 50.0 -mm lens can focus on objects located from $1.5 \mathrm{m}$ to an infinite distance away by adjusting the distance between the lens and the film. When the focus is changed from that for a distant mountain range to that for a flower bed at \(1.5 \mathrm{m},\) how far does the lens move with respect to the film?
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