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The Huygens’s theory of light fails to explain:
A. Photoelectric effect
B. Interference
C. Diffraction
D. Reflection and Refraction

Answer
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Hint: Huygens’s principle is used to understand the propagation of light waves. Here, every point on the wave acts as a source of the next spherical wave front. If we draw a line joining the wave fronts we get the new wave formed due to the propagation of the wave.

Complete answer:
The wave front which is used as the source for spherical wave front is called the primary wave front. And the new wave produced is called the secondary wave front, after any time. This secondary wave now acts as the primary wave front, the next set of secondary wave fronts and so on. This law could explain the propagation of both linear and spherical waves.
Initially, Huygens's principles could explain the laws of reflection and refraction. But it could not the rectilinear propagation of light, which deals with the bending of light also known as diffraction and interference.
However, later, Fresnel showed that Huygens's principle could explain the behaviour of light due to diffraction and interference with slight modifications.
Hence clearly, from the given option, Huygens’s principles could explain the properties of light like reflection, reflection, diffraction and interference. Out of the given options, only Photoelectric effect is left. Thus we can say that the Huygens’s theory of light fails to explain the photoelectric effect of light.

So, the correct answer is “Option A”.

Note:
The secondary waves which are formed always travel in the forward direction only. Also note that photoelectric effect is explained with the dual nature of waves. The others, however, talk of only the wave nature of the light.