5. Geometric optics. Image formation.

Question 1

What are geometric optics? Explain the relationship of refractive index and speed in a formula.

Answer 1

Geometric optics:

If light propagates through a slit much larger than its wavelength, then the spreading of the wavefront (phase) may be simplified into a line (= light ray).

Therefore: mathematical abstractions → geometric

Refractive index - speed relationship:

Light travels with lower speed in denser materials

n₁ = c / c₁

Question 2

Explain the phenomenon of light reflection. What is the relationship between angle of incidence and angle of refraction?

Answer 2

Reflection:

when light arrives at the boundary of 2 optically different media and the light stays in the first medium

Features:

• angle of incidence (α) = angle of reflection (α’)
• perpendicular and in the same plane

Question 3

Define refraction, explain the related Snell’s law and illustrate the Fermat’s principle with an example from the animal kingdom

Answer 3

Refraction:

light is refracted as it changes its medium of propagation (n₁ ≠ n₂)

Snell’s law:

indicates the relationship between angle of incidence θ₁, angle of refraction θ₂, the velocities (v₁ / v₂) in the two media, and the indices of refraction (n₂ / n₁)

sin θ₁/sin θ₂ = v₁/v₂ = n₂/n₁

Fermat’s principle:

states that light takes the path of shortest time instead of the shortest distance

→ ex: “path selection” of ants

Question 4

What is total internal reflection? How can the critical angle be calculated?

Answer 4

Total internal reflection:

1. light travels from medium of higher refractive index to a medium of lower refractive index
2. angle of incidence exceeds the critical angle
3. entire incident light is reflected back

Formula for critical angle: n₁ = n₂ * sin β_h

Question 5

What is endoscopy?

Answer 5

Endoscopy:

• visual method to examine internal organs
• used in diagnostics (biopsy) and therapy (cauterization)
• light conducted by optical fibers into **organ **
• total internal reflection: light is reflected inside the fiber (n_core > n_wall)

Question 6

What is a refractometer? Give the formula how to calculate the concentration

Answer 6

Refractometer:

• Optical instrument for measurements of the index of refraction n₁ (< n_prism) of a small amount of transparent liquid
• used for the indirect concentration measurement of a solution component
• Based on the principle of total internal reflection

n₁ = n₀ + k⋅c

Question 7

Explain the different types of images and relate them to magnification

Answer 7

Types of images:

• real image: projected onto a surface
• virtual image: mapped using an accessory lens

⇒ **magnification: **M= i/o

1. o ≤ f: upright, virtual, magnified
2. f < o < 2f: reverse, real, magnified
3. o = 2f: reverse, real, same size
4. o > 2f: reverse, real, diminished

Question 8

Explain image formation and give the meaning of the 3 principle rays

Give the formula for the lens equation and optical power of refractile surface

Answer 8

Image formation may be achieved by using a curved refractile surface (= converging lens).

Principle rays:

• parallel ray: ray parallel to optical axis
• focal ray: ray through focal point
• central ray: ray through center of the lens

Lens equation: D= 1/f = 1/i + 1/o

Optical power of refractile surface: D = (n-n’) / r