Diverging Lens Real Or Virtual

Lenses

vii-26-00

Sections 23.9 - 23.x

Ray diagram for a diverging lens

Consider now the ray diagram for a diverging lens. Diverging lenses come in a few dissimilar shapes, but all diverging lens are fatter on the edge than they are in the middle. A skilful example of a diverging lens is a bi-concave lens, as shown in the diagram. The object in this example is beyond the focal signal, and, equally usual, the place where the refracted rays announced to diverge from is the location of the image. A diverging lens e'er gives a virtual image, because the refracted rays have to be extended back to meet.

Note that a diverging lens volition refract parallel rays so that they diverge from each other, while a converging lens refracts parallel rays toward each other.

An instance

We can use the ray diagram to a higher place to practise an example. If the focal length of the diverging lens is -12.0 cm (f is e'er negative for a diverging lens), and the object is 22.0 cm from the lens and v.0 cm tall, where is the paradigm and how tall is it?

Working out the epitome altitude using the lens equation gives:

This can be rearranged to:

The negative sign signifies that the image is virtual, and on the aforementioned side of the lens as the object. This is consistent with the ray diagram.

The magnification of the lens for this object distance is:

So the image has a peak of 5 x 0.35 = one.75 cm.

Multiple lenses

Many useful devices, such every bit microscopes and telescopes, apply more than than i lens to form images. To analyze any arrangement with more than than ane lens, piece of work in steps. Each lens takes an object and creates an image. The original object is the object for the first lens, and that creates an prototype. That image is the object for the 2d lens, and then on. Nosotros won't use more than 2 lenses, and nosotros can do a couple of examples to encounter how y'all analyze problems like this.

A microscope

A basic microscope is made up of two converging lenses. One reason for using ii lenses rather than only 1 is that it'southward easier to get higher magnification. If you lot want an overall magnification of 35, for instance, yous tin can use one lens to magnify by a factor of 5, and the second by a factor of 7. This is generally easier to do than to get magnification by a factor of 35 out of a unmarried lens.

A microscope arrangement is shown beneath, along with the ray diagram showing how the start lens creates a real image. This image is the object for the second lens, and the image created past the second lens is the one you'd run across when you lot looked through the microscope.

Note that the final image is virtual, and is inverted compared to the original object. This is true for many types of microscopes and telescopes, that the image produced is inverted compared to the object.

Sign convention

The sign convention for lenses is similar to that for mirrors. Again, take the side of the lens where the object is to be the positive side. Because a lens transmits light rather than reflecting it like a mirror does, the other side of the lens is the positive side for images. In other words, if the image is on the far side of the lens as the object, the epitome altitude is positive and the paradigm is real. If the image and object are on the same side of the lens, the image distance is negative and the image is virtual.

For converging mirrors, the focal length is positive. Similarly, a converging lens e'er has a positive f, and a diverging lens has a negative f.

The signs associated with magnification likewise piece of work the same way for lenses and mirrors. A positive magnification corresponds to an upright paradigm, while a negative magnification corresponds to an inverted image. As usual, upright and inverted are taken relative to the orientation of the object.

Note that in certain cases involving more than one lens the object distance tin can be negative. This occurs when the prototype from the starting time lens lies on the far side of the 2d lens; that paradigm is the object for the second lens, and is chosen a virtual object.

An example using the microscope

Allow's use the ray diagram for the microscope and work out a numerical case. The parameters nosotros demand to specify are:

To work out the prototype altitude for the image formed past the objective lens, employ the lens equation, rearranged to:

The magnification of the image in the objective lens is:

So the height of the image is -i.8 ten 1.0 = -i.viii mm.

This image is the object for the 2d lens, and the object distance has to exist calculated:

The paradigm, virtual in this case, is located at a distance of:

The magnification for the eyepiece is:

So the superlative of the concluding image is -1.eight mm x 3.85 = -half-dozen.ix mm.

The overall magnification of the two lens system is:

This is equal to the final height divided past the height of the object, as it should be. Note that, applying the sign conventions, the final epitome is virtual, and inverted compared to the object. This is consequent with the ray diagram.

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