Chapter 10: Wave — Refraction of Light, Lenses and the Human Eye

This chapter explains how light bends when it passes from one transparent medium to another (refraction), how this leads to total internal reflection and dispersion, and how lenses and the human eye use refraction to form images.

A transparent medium is a substance through which light can propagate, such as air, water, or glass. The speed of light is different in different media.

Denser and rarer media can also be identified by observing the change in direction (refraction) of a light ray as it passes from one medium to another.

The process of bending of light, or the change in direction of light, while passing from one optical medium to another is called refraction of light. It is caused by the change in the speed of light while passing from one medium to another. Greater the change in speed, greater the refraction.

A laser beam bends towards the normal when passing from air into water, and away from the normal when passing from water into air.

Refraction of light through a rectangular glass slab, showing the incident ray, refracted ray, emergent ray, angle of incidence, angle of refraction, angle of emergence, and lateral shift.

When light enters a rectangular glass slab from air (rarer to denser), it bends towards the normal. When it leaves the slab from glass to air (denser to rarer), it bends away from the normal by the same angle, so the emergent ray is parallel to the incident ray but is laterally shifted.

Verifying the laws of refraction using a semicircular glass slab, a laser beam, and a protractor to measure angles of incidence and refraction.

The laws of refraction of light are:

This law is called Snell's Law, named after the mathematician Willebrord Snellius, who discovered it.

The refractive index (μ) of a medium (with respect to air or vacuum) is defined as the ratio of the speed of light in air or vacuum (c) to the speed of light in that medium (v):

μ = speed of light in air or vacuum (c) / speed of light in the medium (v)

When light rays from an object under water travel from water (denser) to air (rarer), they bend away from the normal. When these refracted rays are extended backward, they appear to come from a point higher (nearer to the surface) than the object's actual position.

Light rays from an object under water bend away from the normal at the water-air interface, making the apparent depth less than the real depth.

A pencil partially dipped in water appears bent at the water surface due to refraction.

Light from stars passes through several layers of the earth's atmosphere with continuously changing refractive index before reaching an observer's eyes. This causes the light to bend repeatedly (sometimes towards, sometimes away from the normal), which changes the brightness and apparent position of the star continuously. This is why stars appear to twinkle.

Light from a star undergoes successive refractions through different layers of the atmosphere before reaching the observer, causing twinkling.

Because of atmospheric refraction, the sun appears above the horizon even when it is actually still below the horizon.

When light travels from a denser medium to a rarer medium, the angle of refraction (r) is greater than the angle of incidence (i). As the angle of incidence increases, the angle of refraction also increases and can reach a maximum of 90°.

The angle of incidence in the denser medium for which the corresponding angle of refraction in the rarer medium becomes exactly 90° is called the critical angle.

As the angle of incidence in the denser medium (glass) increases, the angle of refraction in air increases until it reaches 90° at the critical angle; beyond this, total internal reflection occurs.

If the angle of incidence in the denser medium becomes greater than the critical angle, the light does not refract into the rarer medium at all — instead, it is completely reflected back into the same (denser) medium. This phenomenon is called total internal reflection (T.I.R.) of light. All laws of reflection apply during this process.

Diamond has a very high refractive index, so its critical angle is very small (24°). This means light entering a diamond easily has an angle of incidence greater than the critical angle at its many cut faces, undergoing multiple total internal reflections before emerging — making the diamond sparkle. A piece of glass cut into the same shape does not sparkle like a diamond because glass has a much larger critical angle (42°), so most light simply refracts out through the opposite face instead of being totally internally reflected.

A cut diamond sparkles because light undergoes multiple total internal reflections inside it due to its very small critical angle.

An air bubble inside water appears to shine like a mirror because light travelling from water (denser) to the air bubble (rarer) undergoes total internal reflection at the surface of the bubble, since the angle of incidence there exceeds water's critical angle.

An air bubble inside water shines like a mirror due to total internal reflection at the water-air bubble interface.

A mirage is an optical illusion, commonly seen as a pool of water on a hot road, caused by total internal reflection of light. On hot days, air layers close to the ground become hotter (and hence optically rarer) than the layers above (which are relatively cooler and denser). Light from tall objects like trees, travelling from the cooler, denser upper layers to the hotter, rarer lower layers, undergoes continuous refraction and eventually total internal reflection at a certain layer where the angle of incidence exceeds the critical angle for that layer. The reflected rays travel upward to the observer's eyes, creating an inverted image that appears to flicker like a reflection in a pool of water.

A mirage on a hot road is caused by total internal reflection of light at hot, less dense layers of air near the ground.

A prism is a three-dimensional solid bounded by rectangular and triangular surfaces. In a right-angled isosceles triangular prism, light entering perpendicular to one face strikes the hypotenuse face at 45°, which is greater than the critical angle of glass (42°), causing total internal reflection. This can reflect light by 90° (using one prism) or by 180° (using two prisms), without losing the intensity of the light.

Total internal reflection in an equilateral triangular prism and in a right-angled isosceles triangular prism.

Devices that use total internal reflection in prisms: periscope, SLR camera, and binoculars.

Fibre optics is a technology of transmitting light through a thin, transparent medium like glass. The thin optical medium used to carry light in fibre optics is called an optical fibre.

Structure of an optical fibre: a core of thin transparent fibres, surrounded by cladding (lower refractive index) and a plastic protective coating.

The core of an optical fibre carries a bundle of thin fibres made of transparent material like glass. The core is surrounded by a cladding made of a material with a lower refractive index than the core. Light is passed into the fibre such that its angle of incidence on the fibre-cladding boundary is always greater than the critical angle. As a result, the light undergoes repeated total internal reflection and travels through the core without escaping through the cladding — even if the fibre is bent — and finally emerges from the other end.

In communication technology, optical fibres transmit signals or data as light waves using the principle of total internal reflection, allowing very high-speed, secure transmission of large volumes of data over long distances (e.g., 1 Gigabyte per second). A single optical fibre can carry thousands of telephone calls simultaneously. In Nepal, optical fibre cables have been laid along highways such as the East–West Highway and the Mid-Hill Highway, connected internationally through India and China.

Endoscopy is a nonsurgical method to examine internal organs. An endoscope, containing two parallel bundles of optical fibres (one to carry light in, one to collect the reflected light), is inserted through the mouth to examine the oesophagus, stomach, and small intestine. Colonoscopy uses a similar instrument inserted through the rectum to examine the colon and large intestine.

Endoscopy examines the digestive system by passing an optical-fibre endoscope through the mouth; colonoscopy examines the colon through the rectum.

Keyhole surgery (laparoscopic surgery) is a procedure in which a surgeon operates inside the body through a small incision using a laparoscope, which contains bundles of optical fibres and a camera to send light into the body and capture images of internal organs on a monitor. It is used to remove damaged organs, take tissue samples (biopsy), and remove gallstones or kidney stones.

Keyhole (laparoscopic) surgery uses a laparoscope with optical fibres to operate through a small incision.

Sunlight, although it looks white, is actually a mixture of seven colours: red, orange, yellow, green, blue, indigo, and violet (remembered as VIBGYOR).

The process in which light splits into its seven constituent colours while passing through a prism (or a similarly shaped object) is called dispersion of light.

White light splits into the seven colours of the visible spectrum (VIBGYOR) while passing through a glass prism.

The band of seven colours arranged in decreasing order of wavelength is called the visible spectrum.

Although all electromagnetic waves travel at the same speed in a vacuum, their speed differs in other media, and this speed depends on wavelength. Among the seven colours, red light has the longest wavelength and travels fastest, while violet light has the shortest wavelength and travels slowest. Because light bends twice when passing through a prism (entering and exiting), the different colours separate by different amounts — red deviates the least (appearing at the top of the spectrum) and violet deviates the most (appearing at the bottom).

A Newton's disc is a disc painted with the seven colours of the spectrum in proportion. When spun at high speed, the seven colours mix and the disc appears white, showing that white light is a combination of seven colours.

A Newton's disc appears white when spun rapidly; two identical prisms placed opposite each other recombine dispersed light back into white light.

Similarly, if the light dispersed by one prism is passed through a second, identical, inverted prism, the seven colours recombine into white light again.

A rainbow is a circular, colourful arc that appears in the sky when the sun is behind water droplets suspended in the air. Each water droplet acts like a tiny prism.

Sunlight refracts on entering a water droplet, undergoes total internal reflection at the far surface, and refracts again on exiting, separating into the seven colours to form a rainbow.

Sunlight entering a spherical water droplet refracts and splits into seven colours. These colours are then totally internally reflected by the far surface of the droplet, and refract again as they exit, forming a rainbow. Red light, which deviates the least, appears at the top, and violet light, which deviates the most, appears at the bottom. A rainbow appears semicircular when observed from the ground but can appear as a full circle when observed from the sky.

A lens is a transparent medium bounded by at least one spherical (curved) surface. When light refracts through such surfaces, it converges to a point or diverges from a point.

There are two main types of lenses:

Sub-types of convex lenses (biconvex, planoconvex, concavo-convex) and concave lenses (biconcave, planoconcave, convexo-concave).

Parallel rays of light converge to the principal focus (F) after passing through a convex lens.

Parallel rays of light diverge after passing through a concave lens; they appear to come from the principal focus (F).

The three standard rays used to construct ray diagrams for convex and concave lenses.

The position, nature, and size of the image formed by a convex lens depend on the position of the object relative to the lens.

SEE Focus: As the object is moved closer to a convex lens (from infinity towards the lens), the size of the image gradually increases.

Light rays passing through a concave lens always diverge after refraction and never physically meet. When these diverging rays are extended backward, they appear to meet at a point, forming a virtual image.

A concave lens always forms a virtual, erect, and diminished image, regardless of the position of the object.

For any position of the object in front of a concave lens, the image formed is always virtual, erect, and diminished, and forms on the same side as the object. This type of image is used, for example, in the lens of a door peephole.

The ability of a lens to converge or diverge light rays is called the power of the lens. A lens with greater curvature (a thicker lens) has a shorter focal length and a greater power to converge or diverge light; a lens with less curvature (thinner) has a longer focal length and lower power.

Mathematically, the power of a lens is the reciprocal of its focal length in metres: P = 1 / f (in metres)

The human eye is a natural optical instrument that forms images of objects by refracting light through a convex lens.

Main parts of the human eye: cornea, pupil, iris, lens, ciliary muscles, retina, and optic nerve.

Rod and cone cells in the retina — rod cells detect brightness (dim light vision), cone cells detect colour.

Although the convex lens forms an inverted image on the retina, our brain inverts it again, so we perceive objects the right way up.

Accommodation of the eye is the process of adjusting the focal length of the eye lens, by relaxation and contraction of the ciliary muscles, according to the distance of the object, so that a clear image always forms on the retina (since the distance between the lens and the retina stays constant).

When viewing a distant object, the ciliary muscles relax and the lens becomes thin (long focal length); when viewing a nearby object, the ciliary muscles contract and the lens becomes thick (short focal length).

For a normal eye, the range of clear vision is from 25 cm to infinity. The near point of the eye can vary depending on age and the condition of the eye.

When light rays from an object are not focused exactly on the retina, the image appears blurry — this is called a defect of vision. There are two main types: shortsightedness (myopia) and long-sightedness (hypermetropia).

In myopia, nearby objects are seen clearly, but distant objects appear blurry because their images form in front of the retina instead of exactly on it.

In myopia, light rays from a distant object are focused in front of the retina, often because the eyeball is elongated.

Correction: A diverging (concave) lens of suitable focal length is placed in front of the eye. This lens diverges the incoming parallel rays slightly before they enter the eye, so that after refraction by the cornea and eye lens, they focus exactly on the retina.

Myopia is corrected using a concave (diverging) lens placed in front of the eye.

In hypermetropia, distant objects are seen clearly, but nearby objects appear blurry because their images form behind the retina.

In hypermetropia, light rays from a nearby object are focused behind the retina, often because the eyeball is too short or the ciliary muscles cannot contract enough.

Correction: A converging (convex) lens of suitable focal length is placed in front of the eye. This lens converges the incoming rays from nearby objects to some extent before they enter the eye, so that after refraction, they focus exactly on the retina.

Hypermetropia is corrected using a convex (converging) lens placed in front of the eye.

A contact lens is a thin artificial lens worn directly on the cornea (over the tear film), covering the iris and pupil. Since it sits very close to the eye, a contact lens of lower power can replace a much thicker glass lens, and it does not distort peripheral vision the way thick spectacle lenses can. Contact lenses require careful handling — hands must be washed before wearing or removing them, they must be cleaned and disinfected regularly, and should not be worn overnight, to prevent infection.

A contact lens is worn directly on the surface of the cornea to correct vision defects.

Laser eye surgery corrects vision defects by reshaping the cornea using a special ultraviolet laser called an excimer laser. Flattening the central cornea slightly (using a laser) corrects myopia, while raising the central cornea corrects hypermetropia. LASIK (Laser-Assisted in Situ Keratomileusis) is the most popular technique — a laser beam cuts a thin flap in the cornea, which is then flipped to reshape it, before being replaced.

Laser eye surgery (LASIK) reshapes the cornea using an excimer laser to correct myopia or hypermetropia.

As people age, the crystalline proteins of the eye lens can stick together and become cloudy, preventing light from reaching the retina properly and making objects appear blurry. A grey-coloured spot in the pupil due to this cloudiness is called a cataract. It is common in elderly people, and risk increases with UV exposure, smoking, and diabetes.

A cataract is a cloudy area in the eye's lens; cataract surgery replaces the cloudy lens with an artificial intraocular lens (IOL).

SEE Focus: Cataract surgery involves breaking up the cloudy lens using ultrasound through a small hole in the cornea and removing it, then implanting an artificial intraocular lens. Nepali ophthalmologist Dr. Sanduk Ruit developed a very affordable intraocular lens in 1995, making cataract treatment much cheaper and more accessible.

Colour blindness is the inability of the eyes to distinguish colours, due to a defect in the cone cells of the retina. The retina contains millions of three types of cone cells (blue, red, and green) that help identify colours; if these cone cells don't work properly, colours cannot be distinguished. People with red-green colour blindness cannot distinguish red and green colours. It is mainly hereditary, though it can also occur due to mutations or damage from harmful rays.

A colour blindness test uses patterns of coloured dots (Ishihara-type plates) — a number visible to people with normal colour vision may not be visible to a colour-blind person.

The rod cells of the retina allow us to see in dim light. Night blindness (nyctalopia) is the inability to see well at night or in dim places, caused by a problem with the rod cells. Since the rhodopsin pigment in rod cells is made from a protein and vitamin A, a deficiency of vitamin A in the body is one of the main causes of night blindness. It can also be caused by heredity, disease, or injury.

The cornea plays a very important role in refracting light in the eye — its refractive index is 1.376 and its converging power is about +43 D, accounting for about two-thirds of the eye's total light-refracting capacity. The cornea must be protected from scratches and injuries.

Effects of corneal injuries: corneal ulcer (keratitis), corneal edema (fluid buildup), and keratoconus (cone-shaped cornea).

Normal corneal problems can be cured by proper treatment; if the cornea cannot be cured, it can be replaced through corneal transplantation, using a cornea donated (and preserved) after a donor's death, usually removed within 8 to 12 hours of death for best quality. In Nepal, the Nepal Eye Bank (under Tilganga Eye Institute) collects, stores, and distributes corneas. Corneal degeneration is the second leading cause of blindness in Nepal after cataract.

Corneal transplantation replaces a damaged cornea with a healthy donated cornea.