Light does not travel at the same speed in air, glass, and water. The speed of light in air is 3 X 106 m/s. In water it is 2.25 × 108 m/s and in glass is 2 x 108 m/s. This is because glass is optically denser than water and water is optically denser than air. A medium is said to be denser if speed of light decreases and it is said to be rarer if the speed of light increases.
Light travels in a straight line in a medium. but when a ray of light traveling in one transparent medium falls obliquely on the surface of another transparent medium it travels in other medium in a straight path but different from its initial direction. The change in direction of path of light when it passes from one transparent medium to another is called the refraction of light.
A light ray falling on the surface that separates two medium. \(\angle i\) is the angle of incidence between the incident ray and the normal and \(\angle r\) is the angle of refraction between the refracted ray and the normal. Deviation is the angle between the direction of refracted ray and the direction of the incident ray. Therefore, \(\angle\delta\) = \(\mid \angle i - \angle r \mid\)
Refraction of light obeys two laws known as Snell's laws of refraction.
\(\mu = \frac{3 X 10 ^8ms^{-1}}{2.25 X 10 ^8 ms{-1}} = \frac{4}{3} = 1.33\)
Note: No medium can have a refractive index less than 1.
Refractive index (µ) of some common substances
| Substances | µ | Substances | µ |
| Vacuum | 1.00 | Air | 1.00 |
| Ice | 1.31 | Water | 1.33 |
| Alcohol | 1.37 | Glycerine | 1.47 |
| Ordinary Glass | 1.5 | Kerosene | 1.41 |
Question 1: What are the conditions for a light ray to pass undeviated on refraction.
Solution: There are two conditions - (1) when the angle of incidence equals 0. (2) When the refractive index of both the medium is the same.
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Principle of reversibility If the refractive index of medium 2 with respect to medium 1 is \(_1\mu_2= \frac{sin \ i}{sin \ r}\) and the refractive index of medium 1 with respect to medium 2 is then \(_2\mu_1 = \frac{sin \ r}{sin \ i }\) , then \(_1\mu_2 \times _2\mu_1 = 1\) or we can say \(_1\mu_2 = \frac{1}{_2\mu_1}\) |
Question 1: If the refractive index of glass with respect to air is 3/2, then what is the refractive index of air with respect of glass?
Solution: aµg = 3/2, therefore gµa is \(\frac{1}{^3/_2} = \frac{2}{3}\).
Speed: When a ray of light gets refracted from a rarer to a denser medium, the speed of light decreases while if it is refracted from a denser to a rarer medium, the speed of light increases.
Frequency: The frequency of light depends on the source of light so it does not change on refraction.
Wavelength: The speed of light v in a medium, the wavelength of light λ in that medium and the frequency of light f are related as v = fλ.
When light passes from a rarer to a denser medium, the wavelength decreases and when light passes from a denser medium to a rarer medium the wavelength increases.
(1) The depth of water in a vessel, when seen from the air, appears to be less
The real depth is OS. A ray of light starting from point O falling vertically on the water-air surface, travel straight along SA. Another ray OQ incident on the water-air surface at point Q when passes to air, bends away from the normal NQ and goes along the path QT. When ray QT is produced back, the two refracted rays meet at point P. Thus P is the image of O. Thus to the observer the depth of the vessel appears to be SP instead of SO due to the refraction of light from water to air.
(2) Early sunrise and late sunset
(3) Mirage in desert
Sometimes in deserts, an inverted image of a tree is seen which gives a false impression of water under the tree. This is called mirage. The cause of the mirage is due to refraction of light. As in desert, the sand heats up very quickly that's why the layer of air that is in contact with the sand is heated up. As a result, the air near the ground is warmer than the upper air layers. In other words, upper layers are denser than below them! When a ray of light from the sun after reflection from the top of a tree travels from denser to rarer layer, it bends away from the normal. Thus in refraction at the surface of separation of successive layers, each time the angle of refraction increases and the angle of incidence of ray going from denser to rarer also increases till it reaches 90°. On further increase in the angle of incidence from denser to rarer layer suffers complete reflection and now reflected light travels from rarer to denser medium hence it bends towards the normal at each refraction. On reaching the observer's eye an inverted image of the tree is seen.
When the incident ray AB falls on a glass slab, it is incident on the point of incidence B. The ray AB enters from air to glass, so it bends towards the normal and follows the path BC. When the refracted ray BC again strikes the glass surface at point C, it bends away from the normal as ray travels from glass to air and follow the path CD. The emergent ray CD is parallel to incident ray AB. Thus emergent ray and incident ray are in the same direction but laterally displaced.
A prism is a transparent medium bounded by five plane surfaces with a triangular cross-section. Two opposite surfaces of prism are identical triangles while the other three surfaces are rectangular and inclined on each other.
When a light ray of single color falls on the inclined prism surface, incident ray PQ falls on the prism face, it travels from air to glass so it bends towards the normal and travels through path QR. When refracted ray QR hits the prism face at R another refraction occurs. Now the ray QR enters from glass to air so it bends away from the normal and travels in direction RS. Thus, on passing through the prism, the light ray bends towards the base of the prism.
