Lenses | Research & Encyclopedia Articles

Lenses

A lens is a piece of transparent material shaped such that it bends parallel rays of light. The shape of a lens is a segment of a sphere, plane, or a cone (parabola, hyperbola, or ellipse). The bending of light causes the rays to cross, forming an image. This image can be larger or smaller than the actual object being viewed through the lens. The bending of light as it passes through a medium such as glass or plastic is called refraction. The early Greeks used lenses in magnifying glasses long before the ideas of refraction were understood. Today, lenses are used in many optical instruments, such as cameras, eyeglasses, and movie projectors.

Refraction is the bending of light that occurs when light travels through one medium into another. The amount a light ray is bent depends on the angle the ray makes with the interface between the two materials and the difference in the indices of refraction for the two materials. The index of refraction for a material is related to the velocity of light in that material. Light travels faster through air than through glass or plastic. Refraction is a result of this change in velocity of light.

Lenses can occur in one of two shapes. A lens that is thicker in the middle than at the edges is called a convex or converging lens, and a lens that is thinner in the middle is called a concave or diverging lens. A converging lens causes parallel light rays that pass through it to converge, or come together to a point, after it exits the lens. A diverging lens causes the light to diverge, or separate, after it exits.

Parallel light rays entering a converging lens will be bent to arrive at a point called the focal point. The optical axis of a lens is an imaginary line that passes through the two centers of curvature for the opposite surfaces. If entering light rays are parallel to this axis, the focal point will lie on this axis. If the entering light rays are parallel to each other but at an angle to the optical axis, they will arrive at a point in a plane that is perpendicular to the optical axis. This plane is called the focal plane. A lens has two focal points and two focal planes, each on either side of the lens, since light can travel through the lens in either direction.

Because a diverging lens does not focus light to a point, its focal point has a different definition. A diverging lens creates an image that appears to have originated from a point on the opposite side of the lens. This perceived point is the focal point. The focal length of a diverging lens is the same as that of a converging lens, and is defined as the distance between the center of the lens and its focal point.

A converging lens can produce both a virtual and a real image. A virtual image is one in which the light seems to diverge from the image point, when in fact it does not. An example is the image seen in a mirror. A virtual image occurs in a converging lens when the object is between the focal point and the lens. An example of a converging lens producing a virtual image is when a magnifying glass produces a larger image. The object to be magnified, for example, small print in a book, is placed between the focal point and the magnifying glass. The print appears larger as you look at it through the lens. A virtual image produced by a converging lens is always right-side-up and magnified. If an object is placed far enough away from a converging lens to be past the focal point, the light passing through the lens does converge to a point on the other side of the lens producing a real image. A real image is one in which the light passes through the image point. The real image produced by a converging lens is seen inverted, or upside-down. The size of the image depends on how far away the object is from the focal point. If the object is close to the focal point, the image will appear larger (it will focus farther away) than if the object is far from the focal point. The object viewed is always on the opposite side of the lens as its image. An example of a converging lens producing a real image is when a camera lens focuses an image on film.

A diverging lens can only produce a virtual image, because the light passing through a diverging lens never converges to a point. The virtual image produced by a diverging lens is always right-side-up and smaller than the original object. The image and the object viewed are always on the same side of the lens. Diverging lenses are used as viewfinders in cameras.

The image size and distance from the lens can be calculated using the following equation, called the thin-lens equation: 1/p + 1/q = 1/f, where p is the distance from the object to the lens, q is the distance from the image to the lens, and f is the focal length for the lens. Certain sign conventions apply to the thin lens equation. The image distance, q, has a positive value for real images, and a negative value for virtual images. Likewise, the object distance, p, is positive for real objects and negative for virtual objects.

The magnification of a lens can also be calculated using this equation: M = h'/h = -q/p, where M is the magnification, h' is the image height, and h is the object height. The same sign conventions for the thin-lens equation apply to the magnification equation. If the magnification is less than one, the image is smaller than the object. If the magnification is greater than one, the image is larger than the object. If the magnification is equal to one, the image is the same size as the object. A negative value for magnification means the image is real and inverted, and a positive value means the image is upright and virtual.

Lenses are used in many optical instruments such as magnifying glasses, cameras, telescopes, microscopes, and movie projectors. Lenses can be combined in compound optical instruments, such as the compound microscope. In this situation, the image of the first lens acts as the object for the second lens. This arrangement produces a better image because the second lens produces parallel rays that then enter the eye.