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On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygen’s principle leads us to conclude that as it travels the light beam

(A) becomes narrower

(B) goes horizontally without any deflection

(C) bends downwards

(D) bends upwards

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Last updated date: 06th Sep 2024
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Answer
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Hint: Huygen’s principle states that each point on a wavelet acts as a secondary source of waveforms. Refractive index is the ratio of velocity of light in vacuum to the velocity of light in medium. According to the condition, the refractive index increases as height increases and vice versa.


Complete step by step answer:

According to Huygen's principle, light consists of waveforms and each point on a waveform, called a wavelet, acts as a secondary source. Each wavelet also acts as a source of new wavelets expanding in all directions. 


Refractive index is the ratio of the velocity of light in a vacuum to the velocity of light in a medium.

Given that, the refractive index of air changes with height from the ground, as the height increases, the refractive index also increases. 


Now, we have a situation where a light beam was directed to propagate through the medium horizontally. Here, all the points in contact with the horizontal beam of light behave as a source of light. Thus the secondary rays which are propagating from a rarer medium to a denser medium will tend to bend towards the normal. Hence, the beam of light propagating horizontally will bend upwards. 


So, the correct answer is “Option D”.


Note: The refractive index is a unitless quantity as it is the ratio of two similar units. It is inversely proportional to the wavelength. The phenomenon of bending of light that takes place when light moves from one medium to another is called refraction. When deflection takes place the wavelets change their direction of propagation.