Tru Physics

Chapter 2: Magnification

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2.1 Introduction to Magnification

In optics, magnification is the factor by which an object’s size appears larger or smaller than its actual size when viewed through an optical instrument, such as a lens or mirror. Magnification can be expressed as a dimensionless value or as a ratio of the size of the image to the size of the object.

Magnification through a sightseeing telescope.

2.2 Linear Magnification

Linear magnification, often represented as M, is defined as the ratio of the height of the image (h_i) to the height of the object (h_o):

M = \dfrac{h_i}{h_o}

For lenses and mirrors, the magnification can also be expressed as the ratio of the image distance (s_i) to the object distance (s_o):

M = -\dfrac{s_i}{s_o}

The negative sign indicates that the image is inverted with respect to the object.

2.3 Angular Magnification

Angular magnification is used to describe the magnifying power of optical instruments, such as telescopes and microscopes, where the angle subtended by the image at the observer’s eye is compared to the angle subtended by the object when viewed without the instrument. The angular magnification is given by:

M_\text{angular} = \dfrac{\theta_i}{\theta_o}

where \theta_i is the angle subtended by the image and \theta_o is the angle subtended by the object.

2.4 Magnification in Optical Systems

Optical systems often involve a combination of lenses and mirrors, which can produce multiple stages of magnification. The total magnification of an optical system is given by the product of the magnifications at each stage:

M_{\text{total}} = M_1 \cdot M_2 \cdot ... \cdot M_n

2.5 Telescopes

In a telescope, the objective lens or mirror forms a real, inverted image of the object, while the eyepiece lens magnifies this image, creating a virtual, enlarged image for the viewer. The angular magnification of a telescope can be expressed as:

M_{\text{telescope}} = \dfrac{f_{\text{objective}}}{f_{\text{eyepiece}}}

where f_\text{objective} is the focal length of the objective lens or mirror, and f_\text{eyepiece} is the focal length of the eyepiece lens.

2.6 Microscopes

The magnification of a compound microscope is the product of the magnifications of its objective and eyepiece lenses:

M_\text{microscope} = M_\text{objective} \cdot M_\text{eyepiece}

Chapter Summary

In summary, magnification is a crucial concept in understanding how optical instruments, such as lenses, mirrors, telescopes, and microscopes, manipulate the size of images. Knowledge of linear and angular magnification, as well as the magnification in optical systems, helps to design and analyze these devices for various applications in science, engineering, and daily life.

Continue to Chapter 3: Interference

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