Optic Refraction of Light 

Light seems to travel along straight-line paths in a transparent medium. When light enters from one transparent medium to another, it changes its direction. This we can recall from our day-to-day experiences. You might have observed that the bottom of a tank or a pond containing water appears to be raised. Similarly, when a thick glass slab is placed over some printed matter, the letters appear raised when viewed through the glass slab. You might have seen a pencil partly immersed in water in a glass tumbler. It appears to be bent at the interface of air and water. You might have observed that a lemon kept in water in a glass tumbler appears to be bigger than its actual size, when viewed from the sides. All these day-to-day experiences are based on a phenomenon called ‘Refraction’. 

1.0Principle of Least Time

We all know that light ordinarily travels in straight lines. In going from one place to another, light will take the most efficient path and travel in a straight line. 

This is true if there is nothing to obstruct the passage of light between the places under consideration. If light is reflected from a mirror, the bend in the straight-line path is described by a simple formula. If light is refracted, as when it goes from air into water, still another formula describes the deviation of light from the straight-line path. Before thinking of light with these formulas, we will first consider an idea that underlies all the formulas that describe light paths. This idea, which was formulated by the French scientist Pierre Fermat in about 1650, is called Fermat's principle of least time. Fermat's idea was this : 'Out of all possible paths that light might travel to get from one point to another, it travels the path that requires the shortest time.'

Now, light travels at different speeds in different materials. The speed of light is lower in water as compared to the speed of light in air. It is a common observation that a ray of light bends and takes a longer path when it enters into water at an oblique angle. But the longer path taken is actually the path requiring the least time. A straight-line path would take a longer time to reach a certain point in water while a change in path allows the light to reach the same point in least time.        

This is because light travels the path that requires the shortest time i.e., the principle of least time. The amount of change in the direction of light (i.e., the bending of light) depends on the speeds of light in air and in water. This bending of light while passing obliquely from one medium to another is what we call the process ‘refraction’. 

2.0Refraction of Light 

When a ray of light travels obliquely from one transparent medium to another, it bends while crossing the surface separating the two media.

The phenomenon of change in path of light when it passes from one medium to another is called ‘refraction’.

The speed of light is maximum in vacuum, it is about 3 × 10⁸ m/s. The speed of light in air is almost equal to the speed of light in vacuum. 

Some basic terms

Incident ray :  The ray of light falling on the surface of a transparent medium is called ‘incident ray’.

Refracted ray : The ray of light which bends after passing through a transparent medium is called ‘refracted ray’.

Angle of incidence : Angle made by the incident ray with the normal at point of incidence is called ‘angle of incidence’.

Angle of refraction : Angle made by the refracted ray with the normal at point of incidence is called ‘angle of refraction’.

Optically rarer medium  : A transparent medium in which the speed of light is more is called ‘optically rarer medium’ (or simply ‘rarer medium’).

Optically denser medium : A transparent medium in which the speed of light is less is called optically denser medium (or simply ‘denser medium’).

Cause of refraction : The bending of light takes place when it passes from one medium to another because the speed of light changes from one medium to another. Speed of light is different in different media.

Light is a transverse wave 

A transverse wave is a wave where the movement of the particles of the medium is perpendicular to the direction of propagation of the wave (see figure).

3.0Frequency, Wavelength and Speed of a Wave

Wavelength

The minimum distance in which a wave repeats itself is called its wavelength. Also, the distance travelled by a wave when it completes its one cycle is called its wavelength. It is represented by a Greek symbol 'λ' called lambda. It is measured in metres.

The wavelength in a transverse wave refers to the distance between peaks of  two consecutive crests or two consecutive troughs. The length of one complete crest and trough also represents one wavelength of a transverse wave (see figure).

Time Period

The time period T is the time taken by a particle to move through one complete cycle of motion. In other words, time taken to complete one oscillation of a wave is called time period or simply the period of the wave. It is measured in seconds.  

AC and BD also represent wavelength as they are the distances between two consecutive points which are in same state of vibration

For a transverse wave, the time period (T) is the time taken for two successive crests (or troughs) to pass a fixed point. 

Frequency (ν)

The frequency ν is the number of complete cycles or vibrations per unit of time. Also, it can be defined as the number of oscillations per second.

For a transverse wave, the frequency is the number of successive crests (or troughs) passing a given point in 1 second.

Unit of frequency :

Frequency  is measured in cycles per second. The term “cycles” is usually left off and the unit is written as s^–1 or 1/s.

This unit is also called hertz (Hz).   

1 Hz = 1 cycle /sec or 1 oscillation/sec = 1 s^–1 

4.0Relationship Between Time Period and Frequency

Frequency (ν) is the reciprocal of time period (T). That is,

$v=\frac{1}{T}$

Wave speed (v) : Wave speed is distance travelled by the pattern of the wave per unit time. We know that in a time period T, the distance travelled by the wave is one wavelength (λ). Its unit is m/s.

Now, $v=\frac{distance}{time}=\frac{\lambda }{T}=\lambda \left(\frac{1}{T}\right)$ ….(1)

We know that, frequency, $v=\frac{1}{T}$ … (2)

Using (1) and (2), we get, 

v = ν λ

That is, speed = frequency × wavelength

Refraction of Light from Rarer to Denser Medium

When ray of light passes from rarer medium to denser medium, the refracted ray bends towards the normal at the point of incidence [see figure (a)].

Refraction of Light from Denser to Rarer Medium

When ray of light passes from denser medium to rarer medium, the refracted ray bends away from the normal at the point of incidence [see figure (b)].

5.0Laws of Refraction 

(1) The incident ray, the normal to the refracting surface at the point of incidence and the refracted ray, all lie in the same plane (see figure)

(2) The ratio of sine of angle of incidence to the sine of angle of refraction is constant for two given media.

The constant is denoted by n₂₁ and it is called ‘refractive index of medium 2 with respect to medium 1’ (or simply ‘relative refractive index’).  

$\frac{Sini}{Sinr}=constant=n_{21}$

This is called ‘Snell’s Law’.

Refractive index (n₂₁) depends on : 

(1) Nature of pair of media 1 and 2.

(2) Wavelength of the incident light ray. Higher the wavelength, smaller will be the refractive index and vice-versa, valid in case of a dispersive medium (a medium in which waves of different frequencies travel at different speeds). For example, the refractive index is greater for violet light (shorter wavelength) and smaller for red light (longer wavelength).

6.0Angle of Deviation 

The angle through which the incident ray of light is deviated from its original path when it is refracted while passing from one transparent medium to another is called ‘angle of deviation’(δ)  [see figure (a) and (b)].

The angle between incident ray and refracted ray is called ‘angle of deviation’.

An optically denser medium may not possess greater mass density. For example, kerosene having higher refractive index, is optically denser than water, although its mass density is less than water.

Relative Refractive Index of a Medium (n₂₁) 

The relative refractive index of a medium 2 with respect to medium 1 is the ratio of speed of light in medium 1 to the speed of light in medium 2.

$n_{21}=\frac{\text{speed of light in medium 1}}{\text{speed of light in medium 2}}$

_Or $n_{21}=\frac{v_1}{v_2}$

Absolute Refractive Index of a Medium

The ratio of speed of light in vacuum to the speed of light in a medium is called absolute refractive index of medium.

$n=\frac{\text{speed of light in vacuum}}{\text{speed of light in medium}}$

or $n=\frac{c}{v}$

Where, c = speed of light in vacuum ; v = speed of light in medium.

Also, 

$v=\frac{c}{n}orv\alpha \frac{1}{n}$

Greater the value of ‘n’, lesser will be the speed of light, medium will be optically denser. Lesser the value of ‘n’, greater will be the speed of light, medium will be optically rarer. 

Unit of refractive index : Since refractive index (relative or absolute) is a ratio of two speeds, i.e., ratio of two quantities having same units therefore, ‘n’  is a unitless quantity i.e., it has no units.

If the ray of light enters from medium 1 into medium 2 perpendicular to the surface of medium 2, the ray passes undeviated (see figure). That is, no bending of light occurs. In such a case, angle of incidence is zero, ∠i = 0° and ∠r = 0°. According to Snell’s Law, $\frac{sini}{sinr}=n_{21}$

$Orsinr=\frac{sini}{n_{21}}=\frac{sin{0}^o}{n_{21}}=\frac{0}{n^{21}}=0$

Since sin r = 0

∴ ∠ r = 0°

Solved Examples

1. Calculate the refractive index of a diamond if the speed of light in the diamond is 1.24 × 10⁸ m/s. Speed of light in vacuum is 3 × 10⁸ m/s.

Solution

Given, speed of light in vacuum, c = 3 × 10⁸ m/s ; 

speed of light in medium, v = 1.24 × 10⁸m/s ; refractive index, n =?

By definition, $n=\frac{c}{v}=\frac{3\times 10^8}{1.24\times 10^8}=2.42$

2. Light enters from air to glass having refractive index 1.50. What is the speed of light in the glass? The speed of light in vacuum is 3 × 10⁸ ms^–1.

Solution

We know that, absolute refractive index (n) of a medium is given by,

$n=\frac{c}{v}orv=\frac{c}{n}$

Thus, $v_{glass}=\frac{c}{n_{glass}}=\frac{3\times 10^8}{1.5}=2\times 10^{8}m/s$

3. The refractive index of diamond is 2.42. What is the meaning of this statement?

We know that, absolute refractive index (n) of a medium is given by,

$n=\frac{c}{v}orv=\frac{c}{n}$  i.e., $v\alpha \frac{1}{n}$

Since, the refractive index of diamond is 2.42, this suggests that the speed of light in diamond will reduce by a factor 2.42 compared to its speed in air.

Refraction through a glass slab

Let us consider a glass slab bounded by parallel faces XY and X’Y’ (see figure).  A ray of light travelling in air along the path AO gets incident on the face XY. On refraction into glass, it bends towards the normal NN’ and travels along the path OQ. 

The refracted ray OQ strikes the surface X’Y’. At X’Y’, again refraction takes place, the ray of light bends away from normal MM’. This ray is called ‘emergent ray’ and it is parallel to the incident ray. But, there is a shift from initial path (AO) in the emergent ray (QB), called ‘lateral shift’ (d).

Here, the incident ray is parallel to the emergent ray but the incident ray is laterally displaced.

7.0Apparent Depth of Refraction

When an object lying inside an optically denser medium is seen from a rarer medium, its depth appears to be less than its real depth. This depth is called ‘apparent depth’
(see figure). Apparent depth = AI ; real (actual) depth = OA. This happens because rays of light from a denser medium (like water) when enter into rarer medium (like air), they bend away from the normal and thus, they appear to diverge from a point above the object where the image of the object is formed. Thus, we see the image of the object (not the actual object) in water which is at lesser depth than the real depth.

Apparent depth of an object is less than the actual depth when seen from air.

A straight stick when immersed partly in water and held inclined to the surface, it appears to be bent at the point where it enters the water. This apparent bending of stick is also due to the refraction of light when it passes from water into air
(see figure). Length of stick AO is immersed in water, it appears to be bent at point A in the direction AI.

If an object is located in a rarer medium and observer is present in a denser medium, then apparent height is more than the real height. For example, if a fish in water
(denser medium) sees a cat on a platform near the shore, the fish perceives the cat on the platform to be farther from the water’s surface than it actually is [see figure(b)].   

Activity related to apparent depth

1. Place a coin at the bottom of a bucket filled with water. With your eye to a side above water, try to pick up the coin in one go. You will not succeed in picking up the coin.

Reason : When we view this coin from the outside (see figure) , we actually see the image (I) of the coin which is just above the coin (O). If we try to pick up this coin in one attempt, we will not succeed in picking up the coin. This is because we will move our hand to pick up the coin at the location of the image (I) while the coin is located below it.

Activity related to apparent depth

1. Put a coin to the bottom of a large opaque bowl, as shown in figure(a). Stand over the bowl so that you are looking at the coin, and then move backwards away from the bowl until you can no longer see the coin over the bowl’s rim. 

2. Stay at that position and tell your friend to fill the bowl with water, as shown in figure(b). You can now see the coin again because the light is refracted at the water–air interface.

8.0Also Read