Correct Option (c):
Assertion (A) states that a stick dipped in water in a slanting position appears short and bent at the surface of water when observed sideways. This phenomenon is a direct consequence of the refraction of light. When light rays from the submerged part of the stick travel from water (a denser medium) to air (a rarer medium), they bend away from the normal at the water-air interface. This bending causes the apparent position of the submerged part of the stick to be shifted upwards, making it appear bent and shorter than its actual length. Therefore, Assertion (A) is true.
Reason (R) attributes the bent appearance to the scattering of light from water molecules. Scattering of light involves the redirection of light by particles or molecules in a medium, which is responsible for phenomena such as the blue colour of the sky. However, the apparent bending and shortening of an object partially immersed in water are caused by the change in the speed of light as it passes from one medium to another, leading to its refraction. Scattering is not the mechanism responsible for this observation. Therefore, Reason (R) is false.
Since Assertion (A) is true and Reason (R) is false, option (c) is the correct choice.
Incorrect Options:
Options (a) and (b) are incorrect because Reason (R) is false. The phenomenon described in the assertion is due to refraction, not scattering.
Option (d) is incorrect because Assertion (A) is true. The observation of a bent and shortened stick in water is a common and verifiable phenomenon explained by the principles of light refraction.