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Refraction Through Lenses
Because the index of refraction of a lens is greater than air, a ray moves towards the perpendicular as it enters and away as it leaves.
Learning Objectives

Compare the effect of a convex lens and a concave lens on the light rays

Describe the movement of the ray through lens
Key Points
 Recall that the a ray will bend as it enters a medium with a different refractive index. Since the refractive index of a lens is greater than air, a light ray will move towards the perpendicular as it enters and away as it leaves.
 A convex lens has been shaped so that all light rays that enter it parallel to its axis cross one another at a single point on the opposite side of the lens (the focal point). Such a lens is called a converging (or convex) lens for the converging effect it has on light rays. See.
 A concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis. shows the effect it has on rays of light that enter it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens).
 The greater effect a lens has on light rays, the more powerful it is said to be. A powerful converging lens will focus parallel light rays closer to itself and will have a smaller focal length than a weak lens. The power of a lens is given by the equation
$P=\frac{1}{f}$ .
Terms

focal point
A focus—a point at which rays of light or other radiation converge.

convex lens
A lens having at least one convex surface, such that light passing through it, may be brought to a focus.

concave lens
A lens having at least one concave surface, such that light rays passing through it bend away from its optical axis.
Full Text
Refraction Through Lenses
Lenses are found in a huge array of optical instruments, ranging from the simple magnifying glass to a camera lens to the lens of the human eye. The word lens derives from the Latin word for lentil bean—the shape of which is similar to that of the convex lens (as shown in ). The convex lens is shaped so that all light rays that enter it parallel to its axis cross one another at a single point on the opposite side of the lens. The axis is defined as a line normal to the lens at its center (as shown in ). Such a lens is called a converging (or convex) lens for the corresponding effect it has on light rays. The expanded view of the path of one ray through the lens illustrates how the ray changes direction both as it enters and as it leaves the lens.
Since the index of refraction of the lens is greater than that of air, the ray moves towards the perpendicular as it enters, and away from the perpendicular as it leaves (this is in accordance with the law of refraction). Due to the lens's shape, light is thus bent toward the axis at both surfaces. The point at which the rays cross is defined as the focal point F of the lens. The distance from the center of the lens to its focal point is defined as the focal length f of the lens. shows how a converging lens, such as that in a magnifying glass, can concentrate (converge) the nearly parallel light rays from the sun towards a small spot.
Magnifying Glass
Sunlight focused by a converging magnifying glass can burn paper. Light rays from the sun are nearly parallel and cross at the focal point of the lens. The more powerful the lens, the closer to the lens the rays will cross.
The greater effect a lens has on light rays, the more powerful it is said to be. For example, a powerful converging lens will focus parallel light rays closer to itself and will have a smaller focal length than a weak lens. The light will also focus into a smaller, more intense spot for a more powerful lens. The power P of a lens is defined as the inverse of its focal length. In equation form:
shows the effect of a concave lens on rays of light entering it parallel to its axis (the path taken by ray 2 in the figure is the axis of the lens). The concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis. In this case, the lens is shaped so that all light rays entering it parallel to its axis appear to originate from the same point F, defined as the focal point of a diverging lens. The distance from the center of the lens to the focal point is again called the focal length f of the lens. Note that the focal length and power of a diverging lens are defined as negative. For example, if the distance to F in is 5.00 cm, then the focal length is f=–5.00 cm and the power of the lens is P=–20 D. The expanded view of the path of one ray through the lens illustrates how the shape of the lens (given the law of refraction) causes the ray to follow its particular path and be diverged.
In subsequent sections we will examine the technique of ray tracing to describe the formation of images by lenses. Additionally, we will explore how image locations and characteristics can be quantified with the help of a set of geometric optics equations.
Key Term Reference
 Law
 Appears in these related concepts: Newton and His Laws, Gauss's Law, and Models, Theories, and Laws
 Length
 Appears in these related concepts: Mechanical Work and Electrical Energy, Adding and Subtracting Vectors Using Components, and Length
 axis
 Appears in these related concepts: Adding and Subtracting Vectors Graphically, Area Between Curves, and Components of a Vector
 concave
 Appears in these related concepts: Refraction and Magnification, Image Formation by Spherical Mirrors: Reflection and Sign Conventions, and Human Axial Skeleton
 convex
 Appears in these related concepts: Deinococcus and Thermus, Derivatives and the Shape of the Graph, and The Lensmaker's Equation
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 geometric optics
 Appears in this related concept: The Ray Aspect of Light
 index of refraction
 Appears in these related concepts: Combinations of Lenses, Conditions for Wave Interference: Reflection due to Phase Change, and Polarization By Scattering and Reflecting
 inverse
 Appears in these related concepts: Inverse Functions, Hyperbolic Functions, and The Law of Universal Gravitation
 lens
 Appears in these related concepts: Electron Microscopes, Newton's Rings, and The Magnifying Glass
 medium
 Appears in these related concepts: Waves, Painting, and The Role of the Artist
 normal
 Appears in these related concepts: Pumps and the Heart, Vectors in the Plane, and Arc Length and Curvature
 parallel
 Appears in these related concepts: Charging a Battery: EMFs in Series and Parallel, Resistors in Parallel, and Combination Circuits
 perpendicular
 Appears in these related concepts: The Cross Product, Circular Motion, and Normal Forces
 power
 Appears in these related concepts: What is Power?, Sources of Power, and Power
 ray tracing
 Appears in these related concepts: The Thin Lens Equation and Magnification and Thin Lenses and Ray Tracing
 refraction
 Appears in these related concepts: Dispersion of the Visible Spectrum, Aberrations, and The Law of Refraction: Snell's Law and the Index of Refraction
 refractive index
 Appears in these related concepts: PhaseContrast Microscopy, Refraction, and The Speed of Light
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Cite This Source
Source: Boundless. “Refraction Through Lenses.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 10 Oct. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/geometricoptics24/lenses170/refractionthroughlenses61611169/