What this chapter is about
This chapter explains how the human eye works as an optical device. You will learn about the structure of the eye, how it forms images, and how it adjusts to see objects at different distances. The chapter builds on your understanding of lenses from earlier work on light and refraction.
The chapter also covers common vision defects such as myopia, hypermetropia and presbyopia, explaining why they occur and how corrective lenses fix them. You will understand the physics behind these everyday spectacles that millions of people wear.
Finally, the chapter explains atmospheric refraction and the dispersion of white light through a prism. This helps you understand natural phenomena like rainbows, the twinkling of stars, and why the sky appears blue while sunsets appear reddish.
Key ideas
- The human eye uses a convex lens to form a real, inverted image on the retina. The brain interprets this image as upright.
- The ciliary muscles change the curvature of the eye lens to adjust its focal length, allowing the eye to focus on near and distant objects. This ability is called accommodation.
- The least distance of distinct vision for a normal eye is about 25 cm. The far point for a normal eye is at infinity.
- Myopia (short-sightedness) occurs when the image forms in front of the retina. It is corrected using a concave lens.
- Hypermetropia (long-sightedness) occurs when the image forms behind the retina. It is corrected using a convex lens.
- White light splits into seven colours (VIBGYOR) when passing through a prism because different colours have different speeds in glass. This is called dispersion.
- Scattering of light by atmospheric particles causes the blue colour of the sky and the reddish appearance of the sun at sunrise and sunset.
- Atmospheric refraction causes the twinkling of stars and the apparent shift in positions of celestial objects.
Formulas and facts to remember
- Power of a lens: P = 1/f, where f is the focal length in metres and P is in dioptres (D).
- For myopia correction: A concave lens of focal length equal to the defective far point distance is needed.
- For hypermetropia correction: A convex lens is needed so that the near point shifts to 25 cm.
- The angle of deviation in a prism is smallest for yellow-green light and greatest for violet light.
- The order of colours in the visible spectrum by decreasing wavelength: Red, Orange, Yellow, Green, Blue, Indigo, Violet (VIBGYOR when reversed).
- Shorter wavelengths (blue, violet) scatter more than longer wavelengths (red, orange). This is Rayleigh scattering.
- The near point of a young person with normal vision is about 25 cm; for an elderly person, it may be much farther.
Worked examples
Example 1: Finding the power of a corrective lens for myopia
A student cannot see objects clearly beyond 50 cm. What type of lens is needed, and what should be its power?
Solution: The student has myopia because the far point is at 50 cm instead of infinity. A concave lens is needed to diverge light rays so that parallel rays from a distant object appear to come from 50 cm. Focal length required, f = –50 cm = –0.50 m (negative for concave lens) Power, P = 1/f = 1/(–0.50) = –2 D
The student needs a concave lens of power –2 dioptres.
Example 2: Corrective lens for hypermetropia
A person's near point is at 75 cm. Find the power of the lens needed to read a book held at 25 cm.
Solution: The person has hypermetropia. A convex lens must form a virtual image of an object at 25 cm at the person's near point of 75 cm. Object distance, u = –25 cm Image distance, v = –75 cm (virtual image on the same side as the object) Using lens formula: 1/f = 1/v – 1/u 1/f = 1/(–75) – 1/(–25) = –1/75 + 1/25 = (–1 + 3)/75 = 2/75 f = 75/2 = 37.5 cm = 0.375 m Power, P = 1/0.375 = +2.67 D (approximately +2.7 D)
The person needs a convex lens of power about +2.7 dioptres.
Example 3: Understanding dispersion
White light passes through a glass prism. Which colour bends the most and which bends the least? Explain why.
Solution: Violet light bends the most and red light bends the least. This happens because violet light has the shortest wavelength among visible colours, so it travels slowest in glass and refracts most. Red light has the longest wavelength, travels fastest in glass, and refracts least. The difference in bending spreads white light into its component colours, forming a spectrum.
Common mistakes
- Thinking that a convex lens corrects myopia → Myopia needs a concave lens because the image forms too early; diverging rays push the image back to the retina.
- Confusing near point and far point → Near point is the closest distance for clear vision (25 cm normally); far point is the farthest distance (infinity normally).
- Believing the sky is blue because of reflection from oceans → The blue colour is due to scattering of shorter wavelengths by atmospheric molecules, not reflection.
- Forgetting to use correct sign conventions in lens calculations → Always treat distances on the object side as negative and apply the lens formula consistently.
- Thinking stars twinkle because they emit unsteady light → Twinkling is caused by changing atmospheric refraction, not by changes in the star itself.
Quick revision
- The eye lens changes shape to focus; this is accommodation.
- Myopia: image before retina; correct with concave lens.
- Hypermetropia: image behind retina; correct with convex lens.
- Dispersion splits white light because different colours have different speeds in glass.
- Blue sky: blue light scatters more. Red sunrise/sunset: blue scatters away, red reaches us.
- Power of lens in dioptres = 1 ÷ focal length in metres.