How Can A Lens That Is Diverging In Air Be Changed Into A Converging Lens?

How a Lens Refracts Light

Get-go lets consider a double convex lens. Suppose that several rays of light approach the lens; and suppose that these rays of calorie-free are traveling parallel to the chief axis. Upon reaching the front confront of the lens, each ray of calorie-free will refract towards the normal to the surface. At this purlieus, the calorie-free ray is passing from air into a more dense medium (ordinarily plastic or glass). Since the calorie-free ray is passing from a medium in which it travels fast (less optically dense) into a medium in which it travels relatively slow (more than optically dense), it volition curve towards the normal line. This is the FST principle of refraction. This is shown for two incident rays on the diagram below. Once the light ray refracts beyond the boundary and enters the lens, it travels in a straight line until it reaches the back face of the lens. At this boundary, each ray of low-cal will refract abroad from the normal to the surface. Since the low-cal ray is passing from a medium in which it travels tedious (more optically dense) to a medium in which it travels fast (less optically dense), it will bend away from the normal line; this is the SFA principle of refraction.

The higher up diagram shows the beliefs of two incident rays approaching parallel to the chief axis. Note that the 2 rays converge at a point; this point is known as the focal point of the lens. The start generalization that can be made for the refraction of low-cal past a double convex lens is every bit follows:

Refraction Rule for a Converging Lens

Whatever incident ray traveling parallel to the principal axis of a converging lens volition refract through the lens and travel through the focal bespeak on the contrary side of the lens.

Now suppose that the rays of light are traveling through the focal signal on the way to the lens. These rays of light will refract when they enter the lens and refract when they leave the lens. Equally the light rays enter into the more dense lens material, they refract towards the normal; and as they exit into the less dumbo air, they refract abroad from the normal. These specific rays will get out the lens traveling parallel to the chief axis.

The above diagram shows the beliefs of 2 incident rays traveling through the focal point on the way to the lens. Note that the two rays refract parallel to the main axis. A second generalization for the refraction of light by a double convex lens can exist added to the first generalization.

Refraction Rules for a Converging Lens

Whatever incident ray traveling parallel to the master axis of a converging lens will refract through the lens and travel through the focal signal on the opposite side of the lens.
Any incident ray traveling through the focal point on the manner to the lens will refract through the lens and travel parallel to the master axis.

The Sparse Lens Approximation

These ii "rules" will greatly simplify the task of determining the image location for objects placed in front of converging lenses. Equally the rules are practical in the structure of ray diagrams, do not forget the fact that Snells' Law of refraction of light holds for each of these rays. It simply so happens that geometrically, when Snell's Law is applied for rays that strike the lens in the style described above, they will refract in close approximation with these two rules. The tendency of incident light rays to follow these rules is increased for lenses that are thin. For such thin lenses, the path of the light through the lens itself contributes very piddling to the overall change in the direction of the calorie-free rays. Nosotros will use this then-chosen thin-lens approximation in this unit. Furthermore, to simplify the construction of ray diagrams, we will avert refracting each calorie-free ray twice - upon inbound and emerging from the lens. Instead, we will continue the incident ray to the vertical centrality of the lens and refract the light at that point. For thin lenses, this simplification volition produce the same result every bit if nosotros were refracting the calorie-free twice.

Rules of Refraction for Diverging Lenses

Now let'due south investigate the refraction of light by double concave lens. Suppose that several rays of light approach the lens; and suppose that these rays of light are traveling parallel to the principal axis. Upon reaching the front face up of the lens, each ray of low-cal will refract towards the normal to the surface. At this boundary, the light ray is passing from air into a more dense medium (usually plastic or glass). Since the light ray is passing from a medium in which it travels relatively fast (less optically dense) into a medium in which it travels relatively slow (moreoptically dumbo), information technology volition bend towards the normal line. This is the FST principle of refraction. This is shown for two incident rays on the diagram below. Once the light ray refracts beyond the boundary and enters the lens, it travels in a direct line until information technology reaches the dorsum confront of the lens. At this boundary, each ray of light volition refract away from the normal to the surface. Since the lite ray is passing from a medium in which information technology travels relatively slow (more optically dumbo) to a medium in which information technology travels fast (less optically dense), it volition bend abroad from the normal line. This is the SFA principle of refraction. These principles of refraction are identical to what was observed for the double convex lens above.

The above diagram shows the behavior of two incident rays budgeted parallel to the principal axis of the double concave lens. Just like the double convex lens above, calorie-free bends towards the normal when entering and away from the normal when exiting the lens. Yet, considering of the different shape of the double concave lens, these incident rays are non converged to a point upon refraction through the lens. Rather, these incident rays diverge upon refracting through the lens. For this reason, a double concave lens tin never produce a real epitome. Double concave lenses produce images that are virtual. This volition be discussed in more detail in the adjacent part of Lesson five. If the refracted rays are extended backwards behind the lens, an of import observation is made. The extension of the refracted rays volition intersect at a point. This point is known as the focal point. Notice that a diverging lens such as this double concave lens does not really focus the incident light rays that are parallel to the principal axis; rather, information technology diverges these light rays. For this reason, a diverging lens is said to have a negative focal length.

The first generalization can now be made for the refraction of lite by a double concave lens:

Refraction Rule for a Diverging Lens

Whatsoever incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travelin line with the focal point (i.e., in a management such that its extension volition pass through the focal point).

At present suppose that the rays of light are traveling towards the focal point on the way to the lens. Because of the negative focal length for double concave lenses, the calorie-free rays volition head towards the focal point on the reverse side of the lens. These rays will actually achieve the lens before they reach the focal point. These rays of calorie-free will refract when they enter the lens and refract when they get out the lens. Equally the light rays enter into the more dense lens material, they refract towards the normal; and as they leave into the less dense air, they refract away from the normal. These specific rays will leave the lens traveling parallel to the principal centrality.

The above diagram shows the beliefs of two incident rays traveling towards the focal point on the mode to the lens. Note that the 2 rays refract parallel to the principal axis. A second generalization for the refraction of low-cal by a double concave lens can be added to the first generalization.

Refraction Rules for a Diverging Lens

Any incident ray traveling parallel to the principal axis of a diverging lens volition refract through the lens and travelin line with the focal betoken (i.e., in a management such that its extension will pass through the focal point).
Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.

A Third Rule of Refraction for Lenses

The above discussion focuses on the manner in which converging and diverging lenses refract incident rays that are traveling parallel to the master axis or are traveling through (or towards) the focal point. But these are not the only ii possible incident rays. There are a multitude of incident rays that strike the lens and refract in a diverseness of means. Nevertheless, there are three specific rays that carry in a very predictable way. The tertiary ray that we will investigate is the ray that passes through the precise centre of the lens - through the signal where the master axis and the vertical centrality intersect. This ray will refract as information technology enters and refract as information technology exits the lens, but the net effect of this dual refraction is that the path of the light ray is non inverse. For a sparse lens, the refracted ray is traveling in the same management as the incident ray and is approximately in line with it. The behavior of this 3rd incident ray is depicted in the diagram below.

Now we have three incident rays whose refractive behavior is easily predicted. These three rays lead to our threerules of refraction for converging and diverging lenses. These three rules are summarized below.

Refraction Rules for a Converging Lens

Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
Whatsoever incident ray traveling through the focal betoken on the manner to the lens will refract through the lens and travel parallel to the principal centrality.
An incident ray that passes through the center of the lens will in effect go along in the same direction that it had when it entered the lens.

Refraction Rules for a Diverging Lens

Whatsoever incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travelin line with the focal indicate (i.due east., in a direction such that its extension will laissez passer through the focal point).
Any incident ray traveling towards the focal betoken on the way to the lens volition refract through the lens and travel parallel to the principal centrality.
An incident ray that passes through the heart of the lens will in effect continue in the same direction that it had when information technology entered the lens.

These iiirules of refraction for converging and diverging lenses will exist applied through the remainder of this lesson. The rules merely depict the behavior of 3 specific incident rays. While there is a multitude of light rays beingness captured and refracted past a lens, but 2 rays are needed in order to determine the epitome location.