Geometric optics

Содержание и основные понятия

The beam model is applicable when the size of the barrier is much longer than the wave length. It describes images by laws of reflection and refractory.
GEF · 11 grade
PIF · Baseline
Interactive model
Main optical axis
Focus
increase
Aberration
01
The physical picture
What happens and what boundaries the model has.
Main message
The beam model is applicable when the size of the barrier is much longer than the wave length. It describes images by laws of reflection and refractory.
You can get real images on the screen, you can't get fake images.
The linear increase is related to the ratio of size and distance.
The optical systems are built by moving the image from one element to the next.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
1
F
=
1
d
+
1
f
\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
F
1
​
=
d
1
​
+
f
1
​
Thin lens
Γ
=
−
f
d
=
H
′
h
\Gamma=-\frac{f}{d}=\frac{H'}{h}
Γ
=
−
d
f
​
=
h
H
′
​
Linear increase
Review of the situation
The camera focuses the actual inverted image on the matrix, changing the distance between the lens and the sensor.
04
Links and application
In the real world
The camera focuses the actual inverted image on the matrix, changing the distance between the lens and the sensor.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Geometric optical" through the model, not just through the formula.
Outcome 2
Distinguish and correctly use terms: main optical axis, focus, extension.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Main optical axis
Straight through the optical centres of the spherical surface of the lens.
Focus
The point at which parallel rays are collected or from which they appear to be coming out.
increase
Relationship of the linear size of the image to the corresponding size of an object, taking into account the adopted sign.
Aberration
A distortion of the image by the optical system compared to the ideal model of a thin lens.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
1
F
=
1
d
+
1
f
\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
F
1
​
=
d
1
​
+
f
1
​
model effect
Thin lens.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
H
′
h
=
−
f
d
\frac{H'}{h}=-\frac{f}{d}
h
H
′
​
=
−
d
f
​
The beam through the optical centre connects the directional height of the H &apos; image to the mark distance f; the overturned image has H &lt; < 0.
H
′
h
=
1
−
f
F
=
F
−
f
F
\frac{H'}{h}=1-\frac{f}{F}=\frac{F-f}{F}
h
H
′
​
=
1
−
F
f
​
=
F
F
−
f
​
The beam parallel to the main axis passes through the lens through the appropriate focus.
−
f
d
=
1
−
f
F
⇒
1
F
=
1
d
+
1
f
-\frac{f}{d}=1-\frac{f}{F}\Rightarrow\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
−
d
f
​
=
1
−
F
f
​
⇒
F
1
​
=
d
1
​
+
f
1
​
The exclusion of the directional height gives the formula for the thin lens in the agreed sign system.
Conditions:
Thin paraxial lens; d > 0 for a valid object, f > 0 to a valid and f < 0 to an imaginary image, F > 0, to a collecting lens and F < 0 for the diffuse lens.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
Γ
=
−
f
d
=
H
′
h
\Gamma=-\frac{f}{d}=\frac{H'}{h}
Γ
=
−
d
f
​
=
h
H
′
​
model effect
Linear expansion.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
△
A
O
B
∼
△
A
′
O
B
′
\triangle AOB\sim\triangle A'OB'
△
A
OB
∼
△
A
′
O
B
′
The rays through the optical center of the thin lens go almost without deviation, forming similar triangles.
H
′
h
=
−
f
d
\frac{H'}{h}=-\frac{f}{d}
h
H
′
​
=
−
d
f
​
The directional heights and the marked distances are connected minus: the actual overturned image has H < 0.
Γ
:
=
H
′
h
=
−
f
d
\Gamma:=\frac{H'}{h}=-\frac{f}{d}
Γ
:=
h
H
′
​
=
−
d
f
​
By the definition of a marked linear increase, this equality is obtained.
Conditions:
The thin paraxial lens; H\ is the directional height of the image.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that real images can be found on the screen, you cannot get the fake images.
How to Check the Mind
The linear increase is related to the ratio of dimensions and distances. Then check the units, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Geometric optics
The beam model is applicable when the size of the barrier is much longer than the wave length. It describes images by laws of reflection and refractory.
You can get real images on the screen, you can't get fake images.
The linear increase is related to the ratio of size and distance.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.