Refraction of light through at Plane and Curved Surfaces | Jamb(UTME)

Jamb(utme) key points on refraction; law of refraction; refractive index real and apparent depth

Explanation of Refraction in Terms of Velocity of Light

1. Refraction is the bending of light as it passes from one medium to another with different optical densities.
2. The bending occurs because the velocity of light changes in different media.
3. Light travels fastest in a vacuum $(c = 3 \times 10^8m/s)$ and slower in denser materials like water or glass.
4. When light enters a denser medium, it slows down and bends toward the normal.
5. When light moves into a less dense medium, it speeds up and bends away from the normal.
6. The degree of bending depends on the difference in the velocities of light in the two media.
7. Refraction does not occur if light enters a new medium perpendicularly to the surface.
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Laws of Refraction

8. The first law of refraction states that the incident ray, refracted ray, and the normal all lie in the same plane.
9. The second law of refraction is known as Snell’s Law:
   
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   $\frac{\sin i}{\sin r} = constant = n$
10. Here, $(i)$ is the angle of incidence, $(r)$ is the angle of refraction, and $(n)$ is the refractive index.
11. Snell’s law explains how the refractive index determines the amount of bending.
12. The direction of bending (toward or away from the normal) depends on the relative densities of the two media.
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Refractive Index of a Medium

13. The refractive index $(n)$ is a measure of how much light slows down in a medium compared to a vacuum.
14. It is defined as:
    
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    $n = \frac{Speed of Light in Vacuum}{Speed of Light in the Medium}$
15. A higher refractive index means the medium is denser and slows light more.
16. For air, $n \approx 1$, while for water, $n \approx 1.33$, and for glass, $ n \approx 1.5 .
17. The refractive index is dimensionless and always greater than or equal to 1.
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Determination of Refractive Index Using Snell’s Law

18. Snell’s law is used to experimentally determine the refractive index of glass or liquid.
19. A light ray is directed at a known angle $(i)$ toward the surface of the material.
20. The angle of refraction $(r)$ is measured as the ray bends inside the material.
21. The refractive index is calculated using:
    
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    $n = \frac{\sin i}{\sin r}$
22. A rectangular glass block is often used in experiments to measure refractive index.
23. For liquids, a glass tank filled with the liquid is used, and light rays are passed through it at various angles.
24. Snell’s law simplifies the relationship between incident and refracted angles, making calculations straightforward.
25. Accurate measurements of $i$ and $r$ ensure precise refractive index values.
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Real and Apparent Depth

26. The real depth is the actual depth of an object submerged in a medium.
27. The apparent depth is the perceived depth when viewed from above due to refraction.
28. Light rays bend as they leave the denser medium, making objects appear shallower.
29. The apparent depth is always less than the real depth in denser media like water or glass.
30. The relationship is given by:
    
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    $Apparent Depth = \frac{Real Depth}{n}$
31. This phenomenon explains why a pool or fish tank looks shallower than it is.
32. Real and apparent depth are used in optical instruments like microscopes to correct magnification errors.
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Lateral Shift

33. Lateral shift is the sideways displacement of a light ray as it passes through a rectangular glass block.
34. It occurs because the light refracts twice—once when entering and again when exiting the block.
35. The lateral shift increases with the thickness of the block and the angle of incidence.
36. The greater the refractive index of the material, the larger the lateral shift.
37. Lateral shift is used in devices like prisms to direct and manipulate light paths.
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Critical Angle

38. The critical angle is the angle of incidence in a denser medium at which the refracted ray travels along the boundary.
39. It occurs when the angle of refraction equals $90^\circ$.
40. The critical angle is given by:
    
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    $\sin C = \frac{1}{n}$ where $C$ is the critical angle, and $n$ is the refractive index.
41. The critical angle is smaller for media with higher refractive indices.
42. For water $(n = 1.33)$, the critical angle is approximately $48.6^\circ$.
43. For glass $(n = 1.5)$, the critical angle is approximately ( 42^\circ ).
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Total Internal Reflection

44. Total internal reflection occurs when the angle of incidence exceeds the critical angle.
45. In this case, all the light is reflected back into the denser medium, and no refraction occurs.
46. Total internal reflection only happens when light travels from a denser to a less dense medium.
47. It is used in optical fibers to transmit light over long distances with minimal loss.
48. Total internal reflection explains the brilliance of diamonds, as light reflects multiple times inside them.
49. Periscopes and binoculars use prisms to achieve total internal reflection for efficient light redirection.
50. Mirage effects in deserts are caused by total internal reflection of light in layers of air at different temperatures.
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Applications and Practical Examples

51. Refraction allows lenses in eyeglasses to correct vision by bending light to focus properly on the retina.
52. Camera lenses use refraction to focus light and form sharp images.
53. The apparent bending of a stick partially submerged in water is due to refraction.
54. Fiber optics use total internal reflection to transmit signals in telecommunications.
55. Prism spectrometers rely on refraction to separate light into its constituent colors.
56. Rainbows are formed when sunlight refracts through water droplets in the atmosphere.
57. The refractive index of liquids is measured in industries to ensure product quality.
58. Refraction principles are used in designing telescopes and microscopes.
59. Contact lenses are crafted based on the refractive index of the eye’s cornea and lens.
60. The study of critical angles and total internal reflection helps in improving laser and light-based technologies.
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Jamb(utme) key points on glass prism; minimum deviation formula; types of lenses; magnification

Glass Prism

1. A glass prism is a transparent optical element with flat, polished surfaces that refract light.
2. It is typically triangular in shape and made of glass or other transparent materials.
3. When light passes through a prism, it bends due to refraction at each surface.
4. The degree of bending depends on the angle of the prism and the refractive index of the material.
5. A prism can split white light into its constituent colors, creating a spectrum (dispersion).
6. The dispersion occurs because different colors (wavelengths) of light refract at different angles.
7. Prisms are used in spectroscopes to analyze the composition of light sources.
8. A rainbow is a natural example of light dispersion similar to a prism’s effect.
9. Glass prisms are also used in optical devices like periscopes and binoculars for reflecting and redirecting light.
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Use of the Minimum Deviation Formula

10. The minimum deviation occurs when light passes symmetrically through a prism.
11. At minimum deviation, the angle of incidence equals the angle of emergence.
12. The formula for minimum deviation $(\delta_m)$ is:
    
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    $n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$
    where:
    • $n$ = Refractive index,
    • $A$ = Angle of the prism,
    • $\delta_m$ = Minimum deviation angle.
13. This formula allows precise calculation of the prism’s refractive index.
14. Minimum deviation is used in designing optical instruments for maximum accuracy.
15. Measuring $\delta_m$ in experiments helps determine the properties of different transparent materials.
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Types of Lenses

16. Lenses are transparent objects with at least one curved surface, used to refract light.
17. They are classified as converging (convex) and diverging (concave) lenses.
18. A convex lens is thicker in the middle and thinner at the edges.
19. A concave lens is thinner in the middle and thicker at the edges.
20. Convex lenses are also called converging lenses because they focus parallel light rays to a single point (focal point).
21. Concave lenses are called diverging lenses because they spread parallel light rays outward.
22. The focal length $(f)$is the distance between the lens and its focal point.
23. Lenses can form real or virtual images depending on the object’s position relative to the focal length.
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Uses of Convex Lenses

24. Convex lenses are used in magnifying glasses to produce enlarged virtual images.
25. They are used in cameras to focus light onto a film or sensor to capture images.
26. In telescopes, convex lenses magnify distant objects by converging light.
27. Convex lenses are used in eyeglasses to correct farsightedness (hyperopia).
28. Microscopes rely on convex lenses to magnify tiny objects for detailed observation.
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Uses of Concave Lenses

29. Concave lenses are used in eyeglasses to correct nearsightedness (myopia).
30. They are used in peep holes in doors to give a wide-angle view of the outside.
31. Concave lenses are part of complex optical systems in cameras and telescopes.
32. They are also used in combination with convex lenses for fine adjustments in optical instruments.
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Use of the Lens Formula

33. The lens formula relates the object distance $(u)$, image distance $(v)$, and focal length $(f)$:
    
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    $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
34. The lens formula is valid for both convex and concave lenses.
35. All distances are measured from the optical center of the lens.
36. The sign convention for the lens formula depends on the type of lens and the location of the object and image.
37. For convex lenses, $f$ is positive, while for concave lenses, $f$ is negative.
38. The formula helps calculate the position and nature (real or virtual) of the image.
39. By using this formula, you can determine whether an image is magnified, diminished, upright, or inverted.
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Magnification

40. Magnification $(M)$ is the ratio of the height of the image $(h_i)$ to the height of the object $(h_o)$:
    
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    $M = \frac{h_i}{h_o}$
41. Magnification can also be calculated using distances:
    
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    $M = \frac{v}{u}$
42. If $M > 1$, the image is magnified (larger than the object).
43. If $M < 1$, the image is diminished (smaller than the object).
44. For a convex lens, magnification depends on the object’s position relative to the focal point.
45. Concave lenses always produce diminished and virtual images $(M < 1)$.
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Applications of Magnification

46. Magnifying glasses use convex lenses to enlarge small details.
47. Telescopes and microscopes enhance magnification to observe distant or minute objects.
48. Eyepieces in binoculars are designed to magnify the image for a clearer view.
49. In photography, camera lenses adjust magnification to capture objects at varying distances.
50. The concept of magnification is crucial in designing corrective lenses for vision problems.
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