C25_2024_Student

Chapter 25: Optical Instruments

The Human Eye Terminology

  • Near Point: The closest distance at which the eye can focus on an object (approximately 25 cm for a normal eye).

  • Far Point: The farthest distance at which the eye can see clearly (a normal eye can see infinity).

  • Near-Sightedness: Also known as myopia, where distant objects appear blurry due to light being focused in front of the retina.

  • Far-Sightedness: Also known as hyperopia, where close objects appear blurry because light is focused behind the retina.

  • Diopter: A unit of measurement for the optical power of a lens, with positive values indicating converging (convex) lenses and negative values indicating diverging (concave) lenses.

Problem: Near-Sighted Glasses

  • A nearsighted individual requires glasses with a focal length of -20.0 cm, with the lens positioned 1.8 cm from their eye.

  • Conversion to Contact Lenses: To determine the required focal length for contact lenses, the distance from the lens to the eye must be factored in.

Fish’s Eye Vision

  • A fish’s eye is optimized for underwater visibility. When taken out of water:

    • C: He would be nearsighted due to the different refractive properties of air compared to water, affecting his focus.

The Human Eye: Presbyopia

  • As individuals age, the ability of the eye to accommodate decreases.

  • Older Eye: Difficulty focusing on close objects without reading glasses due to reduced ability to bend light effectively.

  • Young Eye: Can focus on close objects without assistance.

Lens Aberrations

  • Spherical Aberration: Caused by spherical lenses where light rays that strike the lens at different distances from the optical axis do not converge at a single point.

  • Chromatic Aberration: Occurs when a lens brings different colors of light to focus at different points due to varying wavelengths.

Mirror Aberrations

  • High-precision optical instruments often utilize mirrors instead of lenses because:

    • Mirrors do not experience chromatic aberration.

    • Parabolic mirrors are engineered to focus light exactly without spherical aberration.

Resolving Power

  • Definition: The ability to distinguish two close objects as separate entities.

  • Resolution Limitations: Limited by diffraction of light, where smaller angles yield better resolution.

Rayleigh Criteria

  • For circular openings:

    • The condition for resolution is given by: sin(θ) = 1.22λ/D

      • Where θ = angle between peaks, λ = wavelength of the electromagnetic wave, D = diameter of the opening.

    • If θ is small, approximations can be used: θ ≈ 1.22λ/D (in radians).

Angle Measurements

  • Trigonometric relationships for small angles:

    • tan(θ) = b/a

    • sin(θ) = b/c

    • For small angles, tan(θ) ≈ sin(θ) ≈ θ in radians.

Problem: Motorcycle Resolution

  • Two motorcycles, separated by 2.00 m, need to be resolved by a detector sensitive to 885 nm radiation at a distance of 10.0 km:

    • Aperture Diameter Calculation: Find the required diameter (D) for resolving the headlights clearly.

Best Distinguishing Between Stars

  • For resolving closely spaced stars, the effectiveness depends on:

    • A) Using a large lens with blue light for better resolution, as shorter wavelengths offer improved resolving capabilities.

Ultimate Resolving Power

  • Limits of resolution:

    • No object can be resolved smaller than about the wavelength of the utilized wave.

    • Visible Light: ~400 nm

    • X-Rays: ~0.01 nm

    • Consideration for structures smaller than 0.01 nm and alternative methods to “see” them.