Effects of Refraction of Light in Everyday Life: Refraction of light can be seen in everyday life in the twinkling of stars, advanced sunrise, delayed sunset, etc. Due to the phenomenon of refraction, the lenses can converge or diverge rays of light passing through them is. We see a pencil broken when dipped in a beaker filled with water due to refraction. If we look around in the surroundings, we can spot many such occurrences that are due to refraction.

We see the world around us during the daytime, but it is tough to see the objects around us on a moonless night when it is dark outside. It is because during the day there is sunlight and on most nights we have a moon in the sky. Sun is the primary source of light. We see an object due to the reflection of light from that object. This is how we see the Moon too! Sunlight is reflected by the Moon, which illuminates the night sky. The twinkling of stars is like a magic trick played by light with our eyes when it travels through different density layers of the Earth’s atmosphere and gets refracted. Most of the phenomena that we see in our everyday lives can be explained by the rectilinear(straight line) motion of light.

Refraction of Light

The bending of the ray of light passing from one medium to the other medium is called refraction. This phenomenon of bending of light from one medium to another occurs due to the different light speeds in various media.

The laws of refraction of light:

1. The incident ray \(\left( {{\rm{IR}}} \right)\), the refracted ray \(\left( {{\rm{RR}}} \right)\) and the normal \(\left( {{\rm{NR}}} \right)\) to the interface of the two transparent media at the point of incidence all lie in the same plane.
2. Snell’s law: The ratio of the sine of the angle of incidence to the angle of refraction\((r)\)
   is a constant called refractive index.  According to this law,
   \(\frac{{\sin \,i}}{{\sin \,r}} = {\rm{constant }}…….{\rm{(1)}}\)
   Where  is the angle of refraction.
   The constant in equation (1) is the refractive index of medium two w.r.t medium one denoted by \({n_{21}}\).

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Refractive Index

The Refractive index of a medium is the characteristic of a medium that decides the speed of light in it. It is a scalar quantity, unit less and dimensionless quantity.

Types of Refractive index

Absolute refractive index	Relative refractive index
(i) Suppose light travels from air to any transparent medium, then \({\rm{R}}.{\rm{I}}{\rm{.}}\) of medium w.r.t. air is called its absolute refractive index i.e. \({}_{{\text{air}}}{\mu _{{\text{medium}}}} = \frac{{\text{c}}}{{\text{v}}}\)	(i) Suppose light travels from medium \((1)\) to medium \((2)\) then \({\rm{R}}.{\rm{I}}{\rm{.}}\) of medium \((2)\) w.r.t. medium \((1)\) is called its relative refractive index  i.e. \(1{\mu _2} = \frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{v_1}}}{{{v_2}}}\) (where \({v_1}\) and \({v_2}\) are the speed of light in medium \(1\) and \(2\) respectively).
(ii) Examples for absolute refractive index   \({}_{\text{a}}{\mu _{{\text{glass}}}} = \frac{3}{2} = 1.5,\) \({}_{\text{a}}{\mu _{{\text{water}}}} = \frac{4}{3} = 1.33,\) \({}_{\text{a}}{\mu _{{\text{diamond}}}} = 2.4,\) \({}_{\text{a}}{\mu _{{\text{crown}}}} = 1.52,\) \({\mu _{{\text{vacuum}}}} = 1,\) \({\mu _{{\text{air}}}} = 1.0003 \approx 1\)	(ii) Examples for relative refractive index   (a) When light enters from water to glass medium: \({}_{\text{w}}{\mu _{\text{g}}} = \frac{{{\mu _{\text{g}}}}}{{{\mu _{\text{w}}}}} = \frac{{\frac{3}{2}}}{{\frac{4}{3}}} = \frac{9}{8}\) (b) When light enters from glass to diamond medium : \({}_{\text{g}}{\mu _{\text{D}}} = \frac{{{\mu _{\text{D}}}}}{{{\mu _{\text{g}}}}} = \frac{{2.4}}{{1.5}} = \frac{8}{5}\)

Note:

1. Cauchy’s equation: \(\mu  = A + \frac{B}{{{\lambda ^2}}} + \frac{C}{{{\lambda ^4}}}\,……….\left( {{\lambda _{{\rm{Red}}}} > {\lambda _{{\rm{Violet}}}}\,{\rm{so}}\,{\mu _{{\rm{Red}}}} < {\mu _{{\rm{Violet}}}}} \right)\)
2. If light travels from medium \((1)\) to medium \((2)\), then \(1{\mu _2} = \frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{{{v_1}}}{{{v_2}}}\)

 Lens

Optical instruments like cameras, projectors, microscopes, binoculars, telescopes etc., have drastically widened our view of the world. Eyeglasses allow millions of people to read and see in comfort. Have you ever wondered which optical component makes all this possible? It is simply a lens!  A lens is a type of transparent material bound by two surfaces, of which at least one is curved.

Applications of Refraction at Spherical Surfaces

Refraction at spherical surfaces finds application in many situations. Some of them are as under:

1. It helps us to estimate the behaviour of the rays of light passing through various lenses like those given in the below picture:
   
2. It helps us understand how light rays will behave while entering the second medium with varying refractive index.

Concave Lens

A lens bounded by two spherical surfaces which curve inwards are called a biconcave or simply a concave lens. It is thinner in the middle than at its edges.

A single piece of glass that curves inwards and diverges the light incident is called a concave lens. Since a concave lens diverges the light rays incident on it, it is also called a diverging lens.

The concave lenses find their application in correcting near-sightedness or myopia. A myopic eye forms the image of a faraway object in front of the retina. A concave lens of suitable focal length brings the image to the retina enabling the person to see it clearly. Concave lenses are also used in the peepholes of the door and the Galilean telescope.

Convex Lens

A lens bounded by two spherical surfaces which bulge outwards is called a biconvex or simply a convex lens. It is thicker in the middle than near the edges.

A single piece of glass that curves outward and converges the incident light is called a convex lens. For different object positions, a convex lens forms images of varying sizes and nature at various locations.

Therefore, these lenses are used in instruments like cameras, telescopes, binoculars, microscopes, projectors, etc., to form images that we see with our human eye, which also has a lens!

Bending of a Pencil in Water

Refraction of light occurs when something gets in the way of the light waves. Like most other materials, light also travels mainly in the form of waves. Because the light can’t travel as quickly in the water as in the air, the light bends around the pencil, causing it to look distorted in the water. The light refraction gives the pencil a slight magnifying effect, making the angle appear more significant than it is, causing the pencil to look crooked.

Normal Shift – Real and Apparent Depth

If the object and the observer are situated in different mediums, then due to refraction, the object appears to be displaced from its real position.

Case 1 – When the Object is in a Denser Medium, and the Observer is in a Rarer Medium

(i) \(\mu = \frac{{{\text{Real}}\,{\text{depth}}}}{{{\text{Appaent}}\,{\text{depth}}}}=\frac{h}{{h’}}\)

(ii) Real depth > Apparent depth

(iii) Shift \(d = h – h’\left( {1 – \frac{1}{\mu }} \right)h\).

For water \(\mu = \frac{4}{3} \Rightarrow d = \frac{h}{4}\);

For glass \(\mu = \frac{3}{2} \Rightarrow d = \frac{h}{3}\)

Case 2 – Object is in Rarer Medium and Observer is in a Denser Medium

(i) \(\mu = \frac{h}{{h’}}\)

(ii) Real depth \(<\) Apparent depth.

(iii) \(d = \left( {\mu  – 1} \right)h\)

(iv) Shift for water \({d_w} = \frac{h}{3}\);  Shift for glass \({d_g} = \frac{h}{2}\)

Refraction Through a Glass Slab

A glass slab is a substance or sheet made of glass material with three dimensions: length, breadth, and height; it is cuboidal shaped.

Lateral Shift Through a Glass Slab

The refracting surfaces of a glass slab are parallel to each other. When a ray of light passes through a glass slab, it is refracted twice at the two parallel faces. Finally, it emerges out parallel to its incident direction, i.e. the ray undergoes no deviation \(\delta  = 0\). The angle of emergence (\(e)\) is the same as the angle of incidence \((i)\).

The perpendicular(normal)  distance between the incident and the emergent ray is the lateral shift of the ray, and it is given by- \(MN = t\,\sec \,r\,\sin \,\left( {i – r} \right)\)

Vertical Shift Through a Glass Slab

When a glass slab is placed in the path of a converging or diverging beam of light, then the point of convergence or divergence appears to be shifted, as shown-

Normal shift \(OO’ = x = \left( {1 – \frac{1}{\mu }} \right)t\)

Refraction of Light Through Prism

Prism is an optically transparent medium bounded by refracting surfaces. The incident surface (on which light ray is incident) and emergent surface (from which light rays emerges) are two dimensional and non-parallel.

When light refracts through a Prism, It is found that- \(A = {r_1} + {r_2}\) and \(i + e = A + \delta \)

For surface \(AC\mu  = \frac{{\sin \,i}}{{\sin \,{r_1}}}\); for surface \(AB\frac{1}{\mu } = \frac{{\sin \,{r_2}}}{{\sin \,e}}\)

Correction of Defects in Human Eye

Myopia (short-sightedness)

A short-sighted eye can see only nearer objects. Distant objects are not seen clearly.
i. In this defect, the image is formed in front of the retina and the far point comes closer.

ii. In this defect, the focal length and radii of curvature of the lens are reduced or the power of the lens increases.
iii. Myopia can be removed by using a concave lens of a suitable focal length.
iv. If the myopic far point is at a distance \(d\) from the eye, then the Focal length of the used lens\(f =  – d =  – \left( {{\rm{defected}}\,{\rm{far}}\,{\rm{point}}} \right)\)
v. A person can see up to distance \( \to x\), wants to see distance \( \to y\left( {y > x} \right)\) so \(f = \frac{{xy}}{{x – y}}\) or power of the lens \(P = \frac{{x – y}}{{xy}}\)

Hypermetropia (long-sightedness)

A long-sighted eye can see distant objects clearly, but nearer objects are not visible.
i. Image is formed behind the retina and near point moves away.

ii. In Hypermetropia, focal length and radii of curvature of lens increases or power of lens decreases.
iii. This defect can be removed by using a convex lens.
iv. If a person cannot see before distance but wants to see the object placed at distance D from the eye, so \(f = \frac{{dD}}{{d – D}}\) and power of the lens \(P = \frac{{d – D}}{{dD}}\)

Presbyopia  

In Presbyopia, both near and far objects are not distinctly visible. It is an old age disease, and it is due to the losing power of accommodation of the human eye. It can be removed by using the bifocal lens.

Astigmatism

In Astigmatism, the eye cannot see horizontal and vertical lines distinctly and simultaneously due to the imperfection in the spherical nature of the eye lens. This defect can be removed by using a cylindrical lens (Torric lenses).

Lens Camera

1. In the lens camera, a converging lens of the adjustable aperture is used.
2. The distance of film from the lens is also adjustable.
3. In photographing an object, the image is first focused on the film by adjusting the distance between lens and film. It is called focusing. After focusing, the aperture is set to a specific value, and then the film is exposed to light for a given time through the shutter.
4. f-number: The ratio of focal length to the aperture of the lens is called the f-number of the camera. \(2,\,2.8,\,4,\,5.6,\,8,\,11,\,22,\,32\) are the f-numbers marked on the aperture. f-number \( = \frac{{{\rm{focal}}\,{\rm{length}}}}{{{\rm{aperture}}}} \Rightarrow {\rm{Aperture}}\,{\rm{\alpha }}\,\frac{1}{{f – {\rm{number}}}}\)

Magnifying Lens

Many times while reading a book, we come across some pretty small words. And it is rather difficult to read such small words. Let us look at a simple but exciting magical instrument. Notice how this instrument converts the small words into big ones. Isn’t it wonderful? When looking through a magnifying lens, objects look bigger than their original size.

Touch the glass lying on the table with your fingers. After moving your hands, when you look at the glass, what do you observe? There is some spot. Next, look at the same glass with a magnifying lens. What do you observe this time? You can also see your fingerprints on the glass. Hence, with the help of a magnifying lens, you can see even those things, which cannot be seen with your naked eyes.

Now, let us look at the history of this simple magnifying lens. In Holland, a man named Anton Van Leeuwenhoek used to work in a cloth store. To check the quality of the clothes, he used magnifying lenses. He used to count the number of threads used in the cloth. Some lenses had the power to magnify 250 times the original size. Later on, he combined these lenses to make an even more powerful instrument called the compound microscope. As years passed, the quality and the shape of the compound microscope kept on improving.

We have the modern-day compound microscope, which has very powerful lenses. These lenses can enlarge an object many times more as compared to simple lenses. Due to this property, the microscope has been of great use to many scientists in discovering many microorganisms and bacteria that cause diseases. Nowadays, the microscope is an essential part of medical laboratories as it can be used in various medical tests to identify the kind of microorganisms in a patient’s body. Based on this identification, medicines are prescribed so that the patient gets well soon. Thus, we can say, the microscope is very helpful for the treatment of the sick. Just as the lenses are helpful in a microscope, they are also used in spectacles for improving vision, cameras, and telescopes for seeing distant objects.

Atmospheric Refraction

The refraction at different layers of the Earth’s atmosphere is called atmospheric refraction. Following are the phenomena that occur due to atmospheric refraction-

1. Apparent flickering of objects placed behind a hot object or fire.
2. Stars near the horizon appear slightly higher than their actual(real) position.
3. Advanced sunrise and delayed sunset.
4. Apparent flattering of Sun’s disc.
5. Twinkling of stars.

1)  Apparent flickering of objects placed behind a hot object or fire
An object placed behind a hot surface or fire appears to flicker when seen through the air. The air above the hot surface becomes light and rises. The upper space is occupied by cool air. Since the refractive index of hot air is less than that of cool air, the physical condition of the medium is not constant. The light appears to come from different directions due to the medium’s changing refractive Index (RI). It results in fluctuation in the apparent position of the object.

2) Stars near the horizon appear slightly higher than their actual position
When seen near the horizon, stars appear somewhat higher than their exact position due to atmospheric refraction.

The refractive index(RI) of the Earth’s atmosphere increases from top to bottom. Therefore, the light coming from a star near the horizon travels from rarer to a denser medium and bends towards the normal. As a result, the star appears higher.

3) Advanced sunrise and delayed sunset
The Sun is visible about two minutes earlier than actual sunrise, and the Sun remains visible for about two minutes after real sunset. When the Sun is below the horizon, the light rays have to pass from rarer to the denser medium of the atmosphere. So, light rays bend towards the normal. Therefore, the Sun appears higher than its actual position.

4) Twinkling of stars
Stars are very far from us, so they behave as a point source of light. Since the physical conditions of the Earth’s atmosphere are flickering, the light from stars appears to come from different directions. This phenomenon results in fluctuation of the apparent position of the star. The amount of light (intensity) coming from stars also vary due to changing refractive Index of the atmosphere layers. The star appears bright when more light from the star reaches our eyes, and the same star appears dull when less light comes to our eyes. Both these effects are responsible for the twinkling of stars.

Summary

1. The refraction of light explains many natural phenomena like twinkling stars, early sunrise and delayed sunset, and the non-twinkling of planets.
2. The refraction of light through a glass slab explains the vertical shift of an object.
3. Refraction of light is applicable in the functioning of lenses used in microscopes, telescopes, binoculars, projectors, cameras, etc.
4. The phenomenon of bending of pencil or straw is due to the refraction of light.

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