CBSE Class 10 Science The Human Eye and The Colourful World NCERT Solutions

The person is experiencing myopia (nearsightedness) because they cannot see distant objects clearly. Myopia occurs when the eye's focal length is too long or the eyeball is too long, causing light to focus in front of the retina instead of on it. This defect is corrected using a concave lens, which diverges light rays before they enter the eye, effectively reducing the eye's overall focusing power. The power of a lens is given by the formula $P\; =\; \backslash frac\{1\}\{f\}$, where $f$ is the focal length in meters. If the person cannot see beyond 2 meters, it means their far point is 2 meters. To correct this, we need a lens that can form a virtual image of an object at infinity at this far point of 2 meters. Thus, the required focal length is $f\; =\; -2$ m (negative for a concave lens). The power of the lens is then $P\; =\; \backslash frac\{1\}\{-2\backslash text\{\; m\}\}\; =\; -0.5$ D. Therefore, a lens with a power of -0.5 D is required.

The correct option is (b).

The student can read the blackboard, which is a distant object, indicating that their far point is normal or adequate. However, they cannot read the textbook, which is a nearby object. This suggests that the near point of their eyes has shifted further away from the eye than the standard 25 cm. This condition is known as hypermetropia (farsightedness). In hypermetropia, the eye's ability to focus on near objects is diminished because the near point has receded. To read the textbook properly, the student would need to hold it further away or use corrective lenses (convex lenses) that increase the converging power of the eye's optical system.

The correct statement is (a).

The phenomenon described is the dispersion of white light by a prism. When white light passes through a prism, it splits into its constituent colors (VIBGYOR - Violet, Indigo, Blue, Green, Yellow, Orange, Red) due to different refractive indices of the prism material for different wavelengths of light. Violet light bends the most, and red light bends the least. The color of the sky is typically blue. We need to determine the orientation of the prism that results in blue being the third color from the top in the dispersed spectrum. In the given figure, case (ii) shows the prism oriented with its base BC at the top. When white light enters such a prism, the colors disperse, with violet bending the most and red the least. The order of colors from the top (least deviated) to the bottom (most deviated) would be Red, Orange, Yellow, Green, Blue, Indigo, Violet. In this arrangement, Blue is indeed the third color from the top.

The correct option is (b).

At noon, the sun is almost directly overhead. This means that sunlight travels through the least amount of Earth's atmosphere to reach our eyes. The scattering of light, particularly the shorter blue wavelengths, is responsible for the sky appearing blue during other times of the day. However, when the sun is at its zenith, the path length through the atmosphere is minimal. While some scattering still occurs, it is not significant enough to remove all the colors or preferentially scatter blue light away to the extent that it colors the sun. Consequently, the sunlight reaches us relatively unscattered, and we perceive it as white light, which is the combination of all colors.

The correct option is (b), interpreted as the differential scattering that colors the sky is minimized, allowing the white light to dominate our perception of the sun.