Lens Formula and Magnification §

Introduction §

The study of lenses, critical in fields like optics, photography, and physics, involves understanding two fundamental concepts: the Lens Formula and Magnification. These principles help in determining the image’s nature, position, and size created by lenses.

Lens Formula §

Definition §

The Lens Formula relates the distance of the image (v), the distance of the object (u), and the focal length of the lens (f). It is given by the equation:

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Types of Lenses §

1. Concave Lens: Thinner at the center than at the edges, diverging light rays.
2. Convex Lens: Thicker at the center than edges, converging light rays.

Applications §

• Used in designing optical instruments like cameras, eyeglasses, and telescopes.
• Calculation of image position in lenses.

Magnification §

Definition §

Magnification is a measure of how much larger or smaller an image is, compared to the object. It’s given by:

$m=\frac{\text{Height of Image}}{\text{Height of Object}}=\frac{v}{u}$

Types §

1. Linear Magnification: Ratio of the height of the image to the height of the object.
2. Angular Magnification: Ratio of the angle subtended by the image at the eye to the angle subtended by the object at the unaided eye.

Applications §

• Determining the size of the image formed by lenses.
• In microscopes and telescopes for magnifying small or distant objects.

Historical Context §

• Invention of Lenses: The use of lenses dates back to ancient Egyptians and Mesopotamians, with the first known lenses made from polished crystal.
• Development of Lens Formula: The scientific understanding of lens behaviour evolved significantly during the Renaissance, culminating in the lens formula’s development.

Examples §

1. Camera Lens: A convex lens in a camera creates a real image on the film or sensor.
2. Eyeglasses: Concave lenses are used in eyeglasses to correct nearsightedness.

Test Questions §

1. For a convex lens of focal length 15 cm, calculate the position of the image when an object is placed 30 cm from the lens.
2. What is the magnification if an image is formed at a distance of 20 cm from a convex lens, with the object placed at 10 cm?
3. Describe how a concave lens would form an image of an object placed at 10 cm from the lens.

For further exploration, you may refer to the following topics in your Obsidian vault:

• Optical Instruments
• Wave Optics
• History of Optics