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 Objective

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

concave lens
A lens having at least one concave surface, such that light rays passing through it bend away from its optical axis.

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

focal point
A focus—a point at which rays of light or other radiation converge.
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: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 Length
 Appears in these related concepts: Atomic Structure, Length, and Introduction to The Sampling Theorem
 axis
 Appears in these related concepts: Area Between Curves, Regional Terms and Axes, and Components of a Vector
 concave
 Appears in these related concepts: Refraction and Magnification, Derivatives and the Shape of the Graph, and Image Formation by Spherical Mirrors: Reflection and Sign Conventions
 convex
 Appears in these related concepts: The Compound Microscope, Human Axial Skeleton, and The Lensmaker's Equation
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 geometric optics
 Appears in this related concept: The Ray Aspect of Light
 index of refraction
 Appears in these related concepts: B.1 Chapter 1, Polarization By Scattering and Reflecting, and B.2 Chapter 2
 inverse
 Appears in these related concepts: Inverse Functions, The Law of Universal Gravitation, and Hyperbolic Functions
 lens
 Appears in these related concepts: The Heisenberg Uncertainty Principle, Newton's Rings, and The Magnifying Glass
 medium
 Appears in these related concepts: Waves, The Role of the Artist, and Repeated Scattering with Low Optical Depth
 normal
 Appears in these related concepts: Vectors in the Plane, Arc Length and Curvature, and Normal Forces
 parallel
 Appears in these related concepts: Resistors in Parallel, Combination Circuits, and How Skeletal Muscles Are Named
 perpendicular
 Appears in these related concepts: The Cross Product, Tangent Vectors and Normal Vectors, and Circular Motion
 power
 Appears in these related concepts: Force of Muscle Contraction, What is Power?, and Authority
 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, The Law of Refraction: Snell's Law and the Index of Refraction, and Aberrations
 refractive index
 Appears in these related concepts: PhaseContrast Microscopy, Refraction, and The Speed of Light
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