Lens and Mirror

Rays of light are focused by a convex lens or a concave mirror, or defocused by a concave lens or a convex mirror. The optical system consisting of lens and mirror is utilized in various equipments and devices, such as a reader of compact discs, a corner mirror, and a telescope. Let us show several fundamental properties of lens and mirror.


Mirror

Since the image in the mirror cannot be projected on a screen, such an image is called virtual image. An image, which can be projected on a screen, is called real image.
The image in the mirror (mirror image) is symmetric in the right- and leftwards, but is not in the up- and downwards.



Concave Mirror

A concave mirror with a smooth surface collects incident parallel rays into a focus.

Cocave mirror
Optical axis, focus, focal length
Mirror formula



Convex Mirror

A convex mirror with a smooth surface diverges incident parallel rays.

Convex mirror
Optical axis, focus, focal length
Mirror formula

(1999-2001 Photo by J. Fukue)



Convex Lens

A convex lens with a smooth surface collects incident parallel rays into a focus.


Convex lens
Cylindrical lens
Optical axis, focus, focal length
Lens formula



Concave Lens

A concave lens with a smooth surface diverges incident parallel rays.

Concave lens
Optical axis, focus, focal length
Lens formula



Gravitational Lens

Gravitational lens is a phenomena, where rays of light from distant objects are bent by the gravitational field of the intervening object and make images at the observer's site. The gravitational lens is a result of Einstein's general relativity.

We can design an optical lens equivalent with a gravitational lens, which has a form like the stem of a wine glass. Such an equivalent glass lens bends parallel rays to produce a double image or a ring image.

Lens appearance
Parallel rays
Double image
Quadruple image
Ring image

‘F-BASIC program (Windows{Internet Explorer)
Try to make a gravitational lens image for various parameters.
Easy gravitational lens

(Photo by J. Fukue)


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