Refraction of Light - Ray Optics and Optical Instruments - Laws of Refraction
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The phenomenon of bending of light as it passes from one medium to another is called refraction.
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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.
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The refractive index (
n) of a medium is given by the formula:n = sin(i) / sin(r), whereiis the angle of incidence andris the angle of refraction. -
When light passes from a rarer medium to a denser medium, it bends towards the normal.
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When light passes from a denser medium to a rarer medium, it bends away from the normal.
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Snell’s law relates the angles of incidence and refraction:
n₁sin(i) = n₂sin(r), wheren₁andn₂are 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.
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The critical angle is defined as the angle of incidence that produces an angle of refraction of 90 degrees.
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TIR is used in fiber optics to transmit information through thin fibers by bouncing light internally.
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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.
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The power of a lens is a measure of its ability to converge or diverge light.
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The power of a lens is given by the formula:
P = 1 / f, wherePis the power of the lens andfis the focal length of the lens. -
The unit of power is dioptre (D).
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Lens formula:
1/f = 1/v - 1/u, wherefis the focal length of the lens,vis the image distance, anduis 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.
- Object distance (
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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/uorm = hₑ/h. -
When
mis positive, the image is erect and virtual. Whenmis 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.
- When lenses are placed in contact, the powers are additive:
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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.
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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
n₁andn₂are 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, whereDis 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, whereλis the wavelength of light used andDis 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.
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