Geometrical (ray) optics

Concave (collecting) spherical mirror: focal distance

$$F = \frac{R}{2}$$

F - focal distance
R - radius of curvature

Find It is known that:

Calculate 'F'

Concave (collecting) spherical mirror

$$\frac{1}{d}+\frac{1}{f} = \frac{1}{F}$$

d - object distance from the mirror (lens)
f - image distance from the mirror (lens)
F - focal distance

Find It is known that:

Calculate 'd'

Concave (collecting) spherical mirror

$$\frac{1}{d}+\frac{1}{f} = \frac{2}{R}$$

d - object distance from the mirror (lens)
f - image distance from the mirror (lens)
R - radius of curvature

Find It is known that:

Calculate 'd'

Convex spherical mirror: zoom

$$\Gamma = \frac{h}{h_0}$$

Γ - linear magnification of the lens
h - image height
h₀ - object height

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Calculate 'Γ'

Convex spherical mirror: zoom

$$\Gamma = \frac{f}{d}$$

Γ - linear magnification of the lens
f - image distance from the mirror (lens)
d - object distance from the mirror (lens)

Find It is known that:

Calculate 'Γ'

Convex spherical mirror

$$\frac{1}{d}-\frac{1}{f} = -\frac{1}{F}$$

d - object distance from the mirror (lens)
f - image distance from the mirror (lens)
F - focal distance

Find It is known that:

Calculate 'd'

Convex spherical mirror

$$\frac{1}{d}-\frac{1}{f} = -\frac{2}{R}$$

d - object distance from the mirror (lens)
f - image distance from the mirror (lens)
R - radius of curvature

Find It is known that:

Calculate 'd'

Light-refraction law

$$\frac{sin(\alpha)}{sin(\gamma)} = n$$

α - incidence angle
γ - refraction angle
n - relative index of refraction

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Calculate 'α'

Absolute index of refraction

$$n = \frac{c}{v}$$

n - absolute index of refraction
c - speed of light
v - speed of light in the environment

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Calculate 'n'

Relative index of refraction

$$n = \frac{n2}{n1}$$

n - relative index of refraction
n1, n2 - absolute indexes of refraction in environments

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Calculate 'n'

Relative index of refraction

$$n = \frac{v_1}{v_2}$$

n - relative index of refraction
v1, v2 - speeds of light in environments

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Calculate 'n'

Light-refraction law: relative indexes of refraction

$$\frac{sin(\alpha)}{sin(\gamma)} = \frac{n2}{n1}$$

α - incidence angle
γ - refraction angle
n1, n2 - absolute indexes of refraction in environments

Find It is known that:

Calculate 'α'

Light-refraction law: speeds of light

$$\frac{sin(\alpha)}{sin(\gamma)} = \frac{v_1}{v_2}$$

α - incidence angle
γ - refraction angle
v1, v2 - speeds of light in environments

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Calculate 'α'

Total reflection

$$sin(\alpha) = \frac{1}{n}$$

α - reflection angle
n - refraction index

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Calculate 'α'

Displacement (shift) of light when crossing the plate

$$b = \frac{d\cdot sin(\alpha-\gamma)}{cos(\gamma)}$$

b - displacement (shift) of light
d - plate thickness
α - incidence angle
γ - refraction angle

Find It is known that:

Calculate 'b'

Angle of deviation (deflection) of light in a prism

$$\delta = \alpha_1+\gamma_2-\phi$$

δ - angle of deflection(deviation)
φ - apical (refracting) angle
α1 - angle of incidence
γ2 - angle of emergence

Find It is known that:

Calculate 'δ'

Angle of deviation (deflection) of light in a prism

$$\delta = \phi\cdot (n-1)$$

δ - angle of deflection(deviation)
φ - apical (refracting) angle
n - refraction index

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Calculate 'δ'

Thin lens formula

$$\frac{1}{F} = (\frac{n1}{n2}-1)\cdot (\frac{1}{R1}+\frac{1}{R2})$$

F - focal distance
n1 - refraction index of the lens
n2 - refraction index of the environment
R1, R2 - radii of curvature of the two surfaces

Find It is known that:

Calculate 'F'

Lens power

$$D = \frac{1}{F}$$

D - lens power
F - focal distance

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Calculate 'D'

Lens power

$$\frac{1}{d}+\frac{1}{f} = D$$

d - object distance from the mirror (lens)
f - image distance from the mirror (lens)
D - lens power

Find It is known that:

Calculate 'd'

Linear magnification of the lens

$$\Gamma = \frac{H}{h}$$

Γ - linear magnification of the lens
H - image height
h₀ - object height

Find It is known that:

Calculate 'Γ'