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A forensic pathologist is viewing heart muscle cells with a microscope that has two selectable objectives with refracting powers of 100 and 300 diopters. When he uses the 100 -diopter objective, the image of a cell subtends an angle of \(3 \times 10^{-3}\) rad with the eye. What angle is subtended when he uses the 300 -diopter objective?

Short Answer

Expert verified
The angle subtended is \(9 \times 10^{-3}\) rad with the 300-diopter objective.

Step by step solution

01

Understanding the Relationship Between Angle and Refractive Power

When using a microscope, the angle subtended by an image at the eye is proportional to the refractive power of the microscope objective in diopters. Therefore, if the refractive power is increased, the angle subtended also increases in direct proportion.
02

Calculating the Angle Subtended with 300 Diopters

Since the angle is directly proportional to the refractive power, we can find the new angle using the formula: \( \text{new angle} = \frac{\text{new refractive power}}{\text{original refractive power}} \times \text{original angle} \). Substituting the values: \( \text{new angle} = \frac{300}{100} \times 3 \times 10^{-3} \text{ rad} = 9 \times 10^{-3} \text{ rad} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Refractive Power
Refractive power is a crucial concept in optics that refers to the ability of a lens to bend or refract light. It is measured in diopters (D), which tell us how much the lens can bend light rays. In the context of a microscope, this is particularly important because the microscope's objective lenses use their refractive power to magnify objects.
When the refractive power increases, it means the lens can bend light more, hence providing more magnification. For example, moving from a 100-diopter lens to a 300-diopter lens would allow for greater magnification of the specimen, enabling the viewer to see smaller details within the specimen.
  • Higher diopters mean greater refractive power and more magnification.
  • Microscope objectives use refractive power to magnify images effectively.
Understanding refractive power helps in selecting the right lens for viewing objects at different levels of detail.
Angle Subtended
In the realm of microscopy, the angle subtended is the apparent angle over which the observer’s eye perceives the image. Imagine this like the piece of the pie your eye sees when you look through the microscope.
The angle changes with the magnification power of the lens used. When the refractive power of the lens increases, so does the angle subtended by the image of the specimen. This occurs because the lens creates a larger image.
  • A larger angle subtended provides a bigger and clearer view of the object.
  • The angle subtended is directly proportional to the refractive power of the objective lens.
In our previous example, using a 300-diopter lens resulted in a larger angle compared to the 100-diopter lens, making the details of the cell more visible.
Diopters
Diopters are a unit of measure used to express the refractive power of lenses, including those used in microscopes. One diopter corresponds to the refractive power of a lens with a focal length of one meter.
They are important because they provide a straightforward way to understand and compare how powerfully lenses can bend light. In microscopy, selecting the appropriate diopter level for the objective lens can drastically change what you see and how well you can see it.
  • Diopters help quantify lens refractive ability.
  • Higher diopters mean greater lens strength for bending light.
They are particularly important in forensic pathology, where precise examination of small details in specimens, such as cells, is essential.
Forensic Pathology
Forensic pathology is a branch of pathology concerned with determining the cause of death by examining a corpse. This typically involves detailed investigations of tissues and organs using microscopes, making the choice of lens magnification crucial.
In forensic pathology, understanding the underlying details in tissues can be critical for discovering evidence or establishing medical facts related to a death case.
  • Microscopes with varying objective magnifications enable pathologists to perform essential detailed analyses.
  • High diopter lenses can aid in examining detailed structures within tissues.
By employing different refractive powers, forensic pathologists can accurately and effectively inspect and interpret samples, which is vital for their work.

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Most popular questions from this chapter

A farsighted man uses eyeglasses with a refractive power of 3.80 diopters. Wearing the glasses \(0.025 \mathrm{m}\) from his eyes, he is able to read books held no closer than \(0.280 \mathrm{m}\) from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?

A farsighted person has a near point that is \(67.0 \mathrm{cm}\) from her eyes. She wears eyeglasses that are designed to enable her to read a newspaper held at a distance of \(25.0 \mathrm{cm}\) from her eyes. Find the focal length of the eyeglasses, assuming that they are worn (a) \(2.2 \mathrm{cm}\) from the eyes and (b) \(3.3 \mathrm{cm}\) from the eyes.

The drawing shows a rectangular block of glass \((n=1.52)\) surrounded by liquid carbon disulfide \((n=1.63) .\) A ray of light is incident on the glass at point A with a \(30.0^{\circ}\) angle of incidence. At what angle of refraction does the ray leave the glass at point B?

An office copier uses a lens to place an image of a document onto a rotating drum. The copy is made from this image. (a) What kind of lens is used, converging or diverging? If the document and its copy are to have the same size, but are inverted with respect to one another, (b) how far from the document is the lens located and (c) how far from the lens is the image located? Express your answers in terms of the focal length \(f\) of the lens.

A glass block \((n=1.56)\) is immersed in a liquid. A ray of light within the glass hits a glass-liquid surface at a \(75.0^{\circ}\) angle of incidence. Some of the light enters the liquid. What is the smallest possible refractive index for the liquid?

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