Optics

# flat diopter

The plane diopter is a refractor system that features two homogeneous, transparent media separated by a surface.

You must have seen an object in a swimming pool and noticed that it doesn’t seem to be where it actually is. You may have also noticed that a spoon in a glass of water appears to be crooked. These two phenomena occur for the same reason: the refraction of light . And this is precisely what happens with a flat diopter.

The flat diopter features two homogeneous, transparent media separated by a flat surface. As an example, we can mention the surface of lakes or swimming pools that separates the water from the air. If we are in one of the two mediums that form the plane diopter, the view we will have of the object in the other medium will be affected by the refraction of light.

The relationship between the position of the object and the position of the viewed image can be obtained if the refractive indices of the two media are known. Look at the following figure:

Scheme of image formation on a flat diopter when the observer is in the least refracting medium

the observer is in the most refractive medium , that is, in the medium where the index of refraction is highest. Note that the light rays come from the bottom of the figure, where the object is located, and the refractive index is n 2 . Point I is where the image is formed, and point O corresponds to the location of the object. We also have d I , which is the distance from the image to the surface, and d O, which is the position of the object to the surface.

Scheme of image formation on a flat diopter when the observer is in the most refracting medium

Note that, in this case, the image formed is much further from the surface than in the previous case, where the observer was in the less refractive medium. In both situations the image formed is virtual.

The equation used to calculate the image position is valid for both situations:

1 = i
n 2      O

The value assigned to an 1 and n 2 will always be relative to the location of the object: n 1 will always be the refractive index of the medium in which the object is located, that is, where the light “comes” from; en 2 will always be the refractive index of the medium where the light goes, which is where the observer is.