Question

The near point of a naked eye is $32 \mathrm{~cm}$. When an object is placed at the near point and viewed by the naked eye, it has an angular size of $0.060$ rad. A magnifying glass has a focal length of $16 \mathrm{~cm}$, and is held next to the eye. The enlarged image that is seen is located $64 \mathrm{~cm}$ from the magnifying glass. Determine the angular size of the image.

   The near point of a naked eye is $32 \mathrm{~cm}$. When an object is placed at the near point and viewed by the naked eye, it has an angular size of $0.060$ rad. A magnifying glass has a focal length of $16 \mathrm{~cm}$, and is held next to the eye. The enlarged image that is seen is located $64 \mathrm{~cm}$ from the magnifying glass. Determine the angular size of the image.

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Physics

John D. Cutnell,… 8th Edition

Chapter 26, Problem 114

Instant Answer

Solved by Expert Adnan Gill

05/04/2020

Step 1

First, we need to find the magnification of the magnifying glass. The magnification (M) can be calculated using the formula: M = 1 + (D/f) where D is the distance of the near point (32 cm) and f is the focal length of the magnifying glass (16 cm). M = 1 + Show more…

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The near point of a naked eye is $32 \mathrm{~cm}$. When an object is placed at the near point and viewed by the naked eye, it has an angular size of $0.060$ rad. A magnifying glass has a focal length of $16 \mathrm{~cm}$, and is held next to the eye. The enlarged image that is seen is located $64 \mathrm{~cm}$ from the magnifying glass. Determine the angular size of the image.

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Key Concepts

Thin Lens Equation

The thin lens equation relates the object distance, image distance, and focal length of a lens. This formula is fundamental in geometrical optics for determining the position and type (real or virtual) of the image produced by a lens. It provides a mathematical framework for understanding how lenses form images and is essential for designing optical instruments.

Near Point of the Eye

The near point of the eye is the closest distance at which an object can be seen clearly without strain. It is an important concept in vision and optics, as instruments like magnifying glasses are designed to adjust the apparent distance of an image so that it falls within the eye's comfortable focusing range.

Angular Magnification

Angular magnification is a measure of how much larger an optical instrument makes an object appear compared to its size when viewed directly. It is defined as the ratio of the angular size of the image as seen through the instrument to the angular size of the object when viewed with the naked eye. This concept is key to understanding the effectiveness of devices like magnifying glasses and microscopes in enhancing visual details.

Angular Size

Angular size refers to the angle that an object subtends at the point of observation. It quantifies the apparent size of an object as seen from a specific position and is typically measured in radians. This concept is crucial in optics because the human eye perceives size based on the angle rather than the object’s actual linear dimensions.

Magnifying Glass

A magnifying glass is a convex lens used to produce a virtual, enlarged image of an object when the object is placed within its focal length. This lens increases the angular size of the object as seen by the eye, thereby making small details more visible. The magnifying glass is a basic optical instrument that illustrates the principles of image formation and angular magnification.

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