NCERT Exemplar · Class 10 Science The Human Eye and the Colourful World

Light refracts mainly at the cornea, passes through the pupil (sized by the iris), and is fine-focused by the convex eye lens onto the retina, which turns the image into nerve impulses the optic nerve sends to the brain. Ciliary muscles vary the lens's curvature -- accommodation: \[P = \dfrac{1}{f} \] For a near object they contract, the lens bulges and \(\displaystyle f\) falls, so \(\displaystyle P\) rises; for a distant object they relax, the lens flattens and \(\displaystyle f\) rises, so \(\displaystyle P\) falls -- the image stays sharp on the retina either way. Answer: Accommodation -- ciliary muscles varying the eye lens's curvature -- lets the eye focus both near and far objects on the retina.

Myopia (short sight): distant objects blur -- their image forms in front of the retina; far point \(\displaystyle x_0\) is nearer than infinity. Hypermetropia (long sight): near objects blur -- their image forms behind the retina; near point \(\displaystyle d\) is farther than $\displaystyle 25$ cm.Myopia -- concave lens brings infinity to the far point: \[u=-\infty,\quad v=-x_0 \] \[\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}=-\dfrac{1}{x_0} \Rightarrow f=-x_0 \] Hypermetropia -- convex lens forms a virtual image of a $\displaystyle 25$ cm object at the near point: \[u=-25\ \mathrm{cm},\quad v=-d \] \[\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{25\ \mathrm{cm}}-\dfrac{1}{d}>0 \quad (d>25\ \mathrm{cm}) \] Answer: Myopia -- concave lens; hypermetropia -- convex lens; each puts the image back on the retina.

At the first face \(\displaystyle AB\), the ray bends towards the normal on entering the denser glass, refracting from \(\displaystyle i_1\) to \(\displaystyle r_1\); inside the prism it travels straight to the second face \(\displaystyle AC\), striking it at \(\displaystyle r_2\). \[A = r_1 + r_2 \] At \(\displaystyle AC\) it bends away from the normal on leaving into air, emerging at angle \(\displaystyle i_2\). Compared with the incident ray's original direction, the emergent ray has turned through the angle of deviation \(\displaystyle D\), measured where the extended incident ray and the emergent ray meet: \[D = (i_1 + i_2) - A \] Answer: The angle of deviation is the angle between the incident ray (produced forward) and the emergent ray.

Sunlight is white, a mix of all wavelengths; air scatters shorter (blue/violet) wavelengths far more than red: \[I_{scatter} \propto \frac{1}{\lambda^4} \]At sunrise/sunset the sun is near the horizon, so its light travels a much longer path through the denser lower atmosphere; almost all the blue/violet scatters out along this path, leaving mostly red to reach the eye directly. At noon the sun is overhead, its light takes the shortest atmospheric path, and little scattering occurs -- most colours arrive together, so the sun looks white. Answer: The long atmospheric path at sunrise/sunset scatters away the blue light, leaving red; the short overhead path at noon scatters little, so the sun looks white.

A prism has two non-parallel refracting surfaces, so unlike a slab the two refractions do not cancel. Each colour in white light has its own refractive index, violet the highest and red the lowest: \[\mu_{violet} > \mu_{red} \Rightarrow \delta_{violet} > \delta_{red} \] At the first face every colour is refracted through a slightly different angle, and this separation is not undone but increased at the second face, so red, orange, yellow, green, blue, indigo and violet emerge along slightly different paths and spread into a continuous band on a screen. Answer: Dispersion is the splitting of white light into the VIBGYOR spectrum because each colour refracts by a different amount, violet most and red least.

Air gets denser toward the ground (pressure rises downward), so its refractive index rises continuously downward: \[n_{atmosphere}\uparrow \text{ (with depth)} \Rightarrow \text{ray bends continuously toward the vertical} \]Starlight entering the atmosphere thus follows a gradually curving path, and the star appears slightly higher than its true position. Along this path the air's density keeps fluctuating, so the bending -- and hence the star's apparent position and brightness -- keeps changing, seen as twinkling. Planets, being far closer, subtend a sizeable angle and act as many neighbouring point sources; their independent fluctuations average out, so planets do not twinkle. Answer: Continuous, fluctuating atmospheric refraction makes a star's point-like light twinkle; a planet's light comes from many such points at once and the fluctuations cancel.