Refraction of Light - Ray Optics and Optical Instruments - Laws of Refraction

• The phenomenon of bending of light as it passes from one medium to another is called refraction.

• Laws of refraction:

  • The incident ray, refracted ray, and the normal to the interface of two media at the point of incidence, all lie in the same plane.
  • The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, known as the refractive index.

• The refractive index (n) of a medium is given by the formula: n = sin(i) / sin(r), where i is the angle of incidence and r is the angle of refraction.

• When light passes from a rarer medium to a denser medium, it bends towards the normal.

• When light passes from a denser medium to a rarer medium, it bends away from the normal.

• Snell’s law relates the angles of incidence and refraction: n₁sin(i) = n₂sin(r), where n₁ and n₂ are the refractive indices of the two media.

• Total Internal Reflection (TIR) occurs when light travels from a denser medium to a rarer medium and the angle of incidence is greater than the critical angle.

• The critical angle is defined as the angle of incidence that produces an angle of refraction of 90 degrees.

• TIR is used in fiber optics to transmit information through thin fibers by bouncing light internally.

• Refraction through a lens:

  • Convex lens: Converging lens that brings parallel incident rays to a focus.
  • Concave lens: Diverging lens that causes parallel incident rays to spread out.

• The power of a lens is a measure of its ability to converge or diverge light.

• The power of a lens is given by the formula: P = 1 / f, where P is the power of the lens and f is the focal length of the lens.

• The unit of power is dioptre (D).

• Lens formula: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance.

• Sign convention:

  • Object distance (u) is positive when the object is on the side of the lens from which the light is coming.
  • Image distance (v) is positive when the image is formed on the side of the lens opposite to the object.
  • Focal length (f) is positive for a convex lens and negative for a concave lens.

• Magnification (m) is the ratio of the height of the image (hₑ) to the height of the object (h).

• Magnification is given by the formula: m = -v/u or m = hₑ/h.

• When m is positive, the image is erect and virtual. When m is negative, the image is inverted and real.

• Power of a combination of lenses:

  • When lenses are placed in contact, the powers are additive: P = P₁ + P₂.
  • When lenses are separated, the powers are subtractive: P = P₁ - P₂.
  • For the net power of more than two lenses, the above formulas can be applied repeatedly.

• Refraction of light through a prism:

  • A prism is a transparent medium bounded by two surfaces, at least one of which is not plane.
  • The deviation produced by a prism depends on the refracting angle (A) and the refractive index (n).
  • The formula for calculation of deviation (δ) is: δ = (n - 1) × A.

• Some common optical defects:

  • Spherical aberration: Caused by the inability of a lens to focus all the parallel rays to a single point due to variations in the refractive index.
  • Chromatic aberration: Caused by the dispersive nature of the refractive index of a lens, resulting in different colors being focused at different distances.
  • Astigmatism: Caused by the unequal curvature of the cornea or the lens, leading to distorted or blurred vision.

End of Slides 1 to 10

Slide 11

• Refraction of light through a glass prism can result in the dispersion of white light into its component colors (rainbow).
• The phenomenon is due to the variation in the refractive index of glass for different wavelengths of light.
• The order of colors in the spectrum, from least deviation to most deviation, are: red, orange, yellow, green, blue, indigo, violet.

Slide 12

• Snell’s law can be used to calculate the angle of refraction when light enters a prism.
• The angle of incidence (i) and the angle of refraction (r) are related by the equation: n₁sin(i) = n₂sin(r).
• The refractive indices n₁ and n₂ are different for different colors of light, leading to dispersion.

Slide 13

• A lens has two focal points: the principal focus (F) and the secondary focus (F’).
• For a convex lens, the principal focus is on the side towards which the light converges.
• For a concave lens, the principal focus is on the same side from which the light diverges.

Slide 14

• Lens aberrations:
  • Spherical aberration: Occurs when parallel rays incident on a lens do not converge to a single point, resulting in a blurred image.
  • Chromatic aberration: Occurs due to the dispersion of light, causing different colors to focus at different distances from the lens.

Slide 15

• The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror.
• The formula is given by: 1/f = 1/v - 1/u.
• The sign convention for mirror formula is the same as that for lens formula.

Slide 16

• Magnification (m) for a mirror is given by the formula: m = -v/u.
• Positive magnification (m > 0) indicates an upright and virtual image.
• Negative magnification (m < 0) indicates an inverted and real image.

Slide 17

• Simple microscope: Consists of a convex lens with short focal length (f) used to enlarge the size of the object.
• Magnifying power (M) of a simple microscope is given by the formula: M = 1 + D/f, where D is the least distance of distinct vision.

Slide 18

• Compound microscope: Consists of a combination of a larger objective lens and a smaller eyepiece lens.
• The object is placed close to the focus of the objective lens.
• The final image formed by the eyepiece becomes large and virtual.

Slide 19

• Telescope: Consists of an objective lens and an eyepiece.
• There are two types of telescopes:
  • Refracting telescope: Uses lenses to gather and focus light.
  • Reflecting telescope: Uses mirrors to gather and focus light.

Slide 20

• The resolving power of an optical instrument is a measure of its ability to distinguish between two closely spaced objects.
• The resolving power (R) is given by the formula: R = 1.22λ / D, where λ is the wavelength of light used and D is the diameter of the objective lens or mirror.

Slide 21

• Dispersion of light is the phenomenon where white light is separated into its constituent colors.
• Dispersion occurs due to the variation in the refractive index of a medium with wavelength.
• Examples of dispersive materials: glass, water, and prisms.

Slide 22

• The colors of light have different wavelengths and frequencies.
• The colors of the visible spectrum, in order of increasing wavelength, are: violet, indigo, blue, green, yellow, orange, and red.
• Each color corresponds to a specific range of wavelengths.

Slide 23

• Chromatic aberration is an optical defect that causes different colors to focus at different distances from a lens or mirror.
• It occurs because the refractive index of a material varies with the wavelength of light.
• Chromatic aberration can be minimized by using a combination of lenses with different refractive indices.

Slide 24

• Spherical aberration is an optical defect that occurs when parallel rays incident on a lens or mirror do not converge to a single point.
• It is caused by the spherical shape of the lens or mirror, which leads to variations in the focal length for different rays.
• Spherical aberration can be minimized by using parabolic mirrors or aspheric lenses.

Slide 25

• Diffraction is the bending of waves around obstacles or through small openings.
• Diffraction of light causes interference patterns, such as the multi-colored fringes observed in soap bubbles or thin films.
• The amount of diffraction depends on the size of the obstacle or opening and the wavelength of the light.

Slide 26

• Huygens’ principle states that every point on a wavefront is a source of secondary wavelets that spread out in all directions.
• Interference of these secondary wavelets gives rise to the phenomenon of diffraction.
• Huygens’ principle helps explain the behavior of waves in various optical systems, such as mirrors and lenses.

Slide 27

• Polarization is a property of transverse waves, such as light waves, where the vibrations occur in a specific direction.
• Polarization can be achieved by using various optical elements, such as polarizing filters or certain crystals.
• Polarized light has several applications, including glare reduction and 3D movie technology.

Slide 28

• Laser is an acronym for “Light Amplification by Stimulated Emission of Radiation.”
• A laser emits a narrow, intense beam of monochromatic (single wavelength) and coherent (in phase) light.
• Lasers have numerous practical applications, including in medicine, communication, industry, and research.

Slide 29

• Fiber optics is a technology that uses thin strands of transparent material, typically glass or plastic, to transmit light signals.
• Light is internally reflected within the fiber-optic cable, allowing it to transmit information over long distances with minimal loss.
• Fiber optics is widely used in telecommunications, internet connectivity, and medical endoscopy.

Slide 30

• Optoelectronics is a branch of physics and technology that deals with the interaction between light and electronic devices.
• Optoelectronic devices, such as light-emitting diodes (LEDs) and photovoltaic cells (solar cells), are the backbone of modern electronic technologies.
• Optoelectronics finds applications in fields such as communication, energy, display technology, and sensing.