Single spherical lens reflection imaging
As shown in the figure, the intersection of the spherical lens and the main optical axis is D, and there is a luminous object e at s on the left side of D. take a beam of light emitted by it as the research object (pink line in the figure), and the light is reflected after passing through a point G on the sphere. Because the reflected light has no intersection with the main optical axis, it cannot form a real image with energy and can be received by the light screen. But we can extend it reversely so that it intersects the main optical axis at h, and its extension line is represented by a dotted line. This is not a real image, because in fact, no light hits the main optical axis behind the lens, but the human eye can see that there seems to be an image. Such an image is called a virtual image.
We stipulate that if the image distance of the virtual image is negative, Manufacturer of spherical lensthe length of DH is actually - s', and the representation of object distance, spherical radius and relevant angle has been given in the figure. Our goal is still to find out the relationship between object distance and image distance.
From the refraction law, we know that the reflection angle = the incident angle, which is shown in the figure as α=γ， Now let's focus on the big triangle △ EGA as we did last time.
Last time we pushed the imaging and imaging of refracted light β Angle, this time we consider the same idea, but now β The angle is not sandwiched between the two triangles as last time, but as the common angle of △ EGA and △ AHG. Therefore, Manufacturer of spherical lens we select the two triangles and list the sine theorem and cosine theorem again:
For △ EGA:
Mark GH = - p ', for △ AHG:
We repeat the old technique and establish two sine theorems together. We get:
Square it on both sides, and then substitute it into the cosine theorem to get:
We found that the imaging of reflection is still consistent with β But there is no "homogeneous point" condition, so we substitute the paraxial condition cos β ≈ 1, after sorting:
This is the paraxial reflection formula of a single sphere.
In addition, according to the computer simulation, Manufacturer of spherical lens the paraxial condition of reflection is much weaker than that of refraction β< At 20 °, the two intersections can be closer.
