NCERT Formulas Class 10 Science Chapter 10 The Human Eye and the Colourful World

👁️ Vision Parameters

Fundamental limits of the normal human eye for distinct vision.

↔ Swipe to view values

Least Distance of Distinct Vision (Near Point): $$D = 25 \text{ cm}$$

Far Point: $$\infty \text{ (Infinity)}$$

Power of Accommodation: Ability of the ciliary muscles to adjust the focal length of the eye lens.

[Image of the structure of the human eye]

👓 Correction of Defects

Using the Lens Formula to calculate the required power for corrective spectacles.

1. Myopia (Short-sightedness): Corrected by Concave Lens.

$$f = -x \quad \text{(where x is the far point)}$$

2. Hypermetropia (Long-sightedness): Corrected by Convex Lens.

$$\frac{1}{f} = \frac{1}{d} – \frac{1}{D} \quad \text{(d = near point of defective eye)}$$

[Image of myopia and hypermetropia correction using lenses]

💎 Glass Prism Phenomena

Refraction through a prism involves the Angle of Deviation ($\delta$).

Angle of Deviation Formula: $$i + e = A + \delta$$

(i = incident angle, e = emergent angle, A = angle of prism)

Dispersion: Splitting of white light into VIBGYOR.

$$\text{Speed in glass: } V_{red} > V_{violet} \implies \delta_{violet} > \delta_{red}$$

[Image of dispersion of white light by a glass prism]

🌍 Atmospheric Phenomena

Caused by the varying refractive index of different layers of the atmosphere.

1. Twinkling of Stars: Due to continuous change in apparent position.

2. Advanced Sunrise / Delayed Sunset: Difference of about 2 minutes.

[Image of atmospheric refraction showing apparent position of stars]

☁️ Tyndall Effect & Scattering

The intensity of scattered light depends on the wavelength ($\lambda$).

Rayleigh Scattering Law: $$\text{Scattering} \propto \frac{1}{\lambda^4}$$

Blue color of sky: Shorter $\lambda$ (blue) scatters more.

Red color of Sun (Sunrise/Set): Longer $\lambda$ (red) reaches the observer.