# 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.

#### 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 (Figure 1).

• A concave lens is a diverging lens, because it causes the light rays to bend away (diverge) from its axis. Figure 3 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

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

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

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

#### Figures

1. ##### Convex Lens

Rays of light entering a converging lens parallel to its axis converge at its focal point F. (Ray 2 lies on the axis of the lens.) The distance from the center of the lens to the focal point is the lens’s focal length f. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

2. ##### 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.

3. ##### Diverging Lens

Rays of light entering a diverging lens parallel to its axis are diverged, and all appear to originate at its focal point F. The dashed lines are not rays—they indicate the directions from which the rays appear to come. The focal length f of a diverging lens is negative. An expanded view of the path taken by ray 1 shows the perpendiculars and the angles of incidence and refraction at both surfaces.

## 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 Figure 1). 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 Figure 1). 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. Figure 2 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.

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:

$P=\frac{1}{f}$

Figure 3 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 in Figure 3 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 Glossary

axis
An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry).
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concave
curved like the inner surface of a sphere or bowl
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concave lens
A lens having at least one concave surface, such that light rays passing through it bend away from its optical axis.
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convex
curved or bowed outward like the outside of a bowl or sphere or circle
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convex lens
A lens having at least one convex surface, such that light passing through it, may be brought to a focus.
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equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
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focal point
A focus—a point at which rays of light or other radiation converge.
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geometric optics
Optics that describes light propagation in terms of "rays".
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index of refraction
For a material, the ratio of the speed of light in vacuum to that in the material.
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inverse
Opposite in effect or nature or order.
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Law
A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
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lens
an object, usually made of glass, that focuses or defocuses the light that passes through it
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light
The natural medium emanating from the sun and other very hot sources (now recognised as electromagnetic radiation with a wavelength of 400-750 nm), within which vision is possible.
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normal
A line or vector that is perpendicular to another line, surface, or plane.
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parallel
An arrangement of electrical components such that a current flows along two or more paths.
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perpendicular
at or forming a right angle (to).
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power
A measure of the rate of doing work or transferring energy.
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ray
A line extending indefinitely in one direction from a point.
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ray tracing
A technique used in optics for analysis of optical systems.
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refraction
Changing of a light ray’s direction when it passes through variations in matter.