## Causes of Refraction of Light

Subject: Science

#### Overview

The change in speed of light when it passes from one medium to another is the cause of the refraction of light. This note gives us further information about causes of refraction of light.
##### Causes of Refraction of Light

The speed of light in air, water, and glass is 3×108 m/s, 2.2 ×108 m/s and 2×108 m/s respectively. The change in speed of light when it passes from one medium to another is the cause of the refraction of light. The medium, through which the light passes is called optical medium. The optical medium, in which the velocity of light is more, is called rarer medium. The medium in which the velocity of light is comparatively less is called denser medium.

Some examples of refraction of light:

1. The apparent upward bending of a pencil when placed in water:

The given figure shows a pencil ABC placed in a trough of water. The pencil appears bent upwards from the point B. Rays CE and CD from the end C of the pencil pass from water to air, and are bent away from the normal along EE’ AND DD’ respectively, since they are passing in rarer medium. To the eye, they appear to come from point C’ above C. C’ is thus the image of C as a result of the refraction. The same reasoning applies to any point on the immersed portion of pencil BC so that the observer sees an image apparently in the position BC.

2. Image of coin in water:

In the given figure, a coin ‘o’ is placed at the bottom of a beaker containing water. Two rays OA and OD from O are refracted along OA and OD from O are refracted along AB and DE respectively. These divergent rays appear to come from ‘I’ which is the virtual image of ‘O’. Clearly, the image ‘I’ is at a less depth than ‘O’. Thus, the coin at ‘O’ appears to rise at ‘I’ when the coin is kept in water. The Same phenomenon explains why a swimming pool appears shallower than it really is.

3. Twinkling of stars:

The light from the stars passes through the atmosphere before it reaches an observer on the earth. Stars twinkles due to change in density whichis in a small range, the image of the star appears to move within a small area in the space and this gives to twinkling effect. Stars do not appear twinkling if they are viewed from above the earth’s atmosphere. Twinkling effect is observed if the stars are viewed from earth’s surface.
##### Real and apparent depth

Let a point object O be placed just below a rectangular glass slab ABCD of thickness AD or BC as shown in the figure. A ray OP incident normally on the surface CD passes to air without deviation along PQ. Ray OS in the glass is refracted along SR in the air. The two rays meet at I when produced back. Thus, ‘I’ is the virtual image of the object ‘O’. Hence, the object at ‘O’ appears raised at ‘I’. When viewed directly the object O through the glass slab. Let ∠OSN = ∠i be the angle of the incidence in the glass and ∠MSR = ∠r be the angle of refraction in the air. Here, PO is real depth and PI is medium, the object appears to be in less depth due to refraction. Such less depth is called apparent depth and the actual depth is called real depth.

##### Things to remember
• The speed of light in air, water, and glass is 3×108 m/s, 2.2 ×108 m/s and 2×108 m/s respectively.
• The change in speed of light when it passes from one medium to another is the cause of the refraction of light.
• The optical medium, in which the velocity of light is more, is called rarer medium.
• The medium in which the velocity of light is comparatively less is called denser medium.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### Real Depth and Apparent Depth
The process of bending of light as it passes from one medium to another medium is called refraction of light.

AO → incident ray
OB → refracted ray
BC → emergent ray
MN and M'N' = normal
∠AOM = Angle of incidence
∠BON = Angle of refraction
The velocity of light in rarer medium is greater than velocity of the light in denser medium. So, because of the variation of speed of light in two medias, the light bends which is the main cause of refraction.
1. A stick partly immersed in water and placed inclined to the surface, appears bent at the surface.
2. A swimming pool appears shallower than it really is.
The laws of refraction are as follows:
1. The incident ray, refracted ray and the normal lies in the same point of a plane.
2. A ray of light bends towards the normal when it travels from rarer medium to denser medium and bends away from the normal when it travels from denser medium to rarer medium.
3. The ratio of sine of angle of incidence (Sin i) to the sine of angle of refraction (sin r) is always constant for a given pair of media.
Mathematically,
= µ (constant)
The constant quantity 'µ' is called refractive index.
The refractive index of a medium is defined as the ratio of velocity light in air (or vacuum) to the velocity of the light in the medium.
∴ RI of a medium =
The refraction of light is shown in the figure.
In the gven figure:
AO → incident ray
OB → refracted ray
BC → emergent ray
MN = normal
∠AOM = Angle of incidence
∠BON = Angle of refraction
Since the refracted ray bends towards the normal we can say light comes from rarer medium (water) and falls to denser medium (glass).
1. The refraction of light is shown in the figure.
2. Due to refraction of light, the light ray coming from the parts of pipe inside the water gets bent at the surface of water. These deviated rays appear on our eyes and the parts of ruler inside the water appear bent.
Due to refraction of light , light rays coming from the bottom of pond, (i.e. denser medium) bends on the surface of water and passes to the air (i.e. rarer medium). These deviated rays reach on our eyes and the bottom of the pond appears slightly upwards than its actual position. As a result, the apparent depth of water in pond is less than its depth.
Due to refraction of light, the light rays coming from the apparent position of the fish appears shorter eyes and he hits the spear at that point but the fish does not get hit because the actual position of the fish is slightly below that of apparent position of the fish.
The atmosphere of the earth contains of layers of air with different densities. Due to wind, the densities change continuously. The rays of the light coming from the stars pass through the atmosphere and get refracted. These refracted rays come to our eyes and we see the stars as twinkling.
The angle of incidence for which the angle of refraction is 900 when light ray passes from denser medium to rarer medium is called critical angle.
Here, c is the critical angle.
When an incident ray of light from denser medium goes to rarer medium with the angle of incidence greater than the critical angle, all the rays of light are reflected back in the denser medium. This phenomenon is called total internal reflection of light.
Necessary conditions:
1. The incident ray must pass from denser medium to rarer medium.
2. The angle of incidence must be greater than the critical angle.
The angle of incidence for which the angle of refraction is 900 when light ray passes from denser medium to rarer medium is called critical angle. Critical angle of glass, water and diamond are as follows:
1. glass = 420
2. water = 490
3. diamond = 240
The relation between refractive index(µ) and critical angle (C) is given by
Refractive index (µ) = Refractive index is inversely proportional to the sine of critical angle.

It means that the ray is passing from glass to air such that the angle of incidence is 420 while the angle of refraction is 900.

1. It is called critical angle and its value is 420.
2. When the ∠IOM is further increased, then there occurs total internal reflection and all the rays reflect in the glass medium.
Optical fibers are very small thread of transparent glass that works as a light pipe. Their main uses are:
1. To view the internal parts of the body as in endoscopy
2. For receiving and transmitting electric signals in cables
Any two effects of total reflection of light are as follows:
1. Mirage
2. Sparkling of diamond

In summer, in the coal tarred roads or in the deserts, optical illusion is observed due to total internal reflection of light. This phenomenon is called mirage.

In a hot sunny day in a summer, air in the ground level gets heated and acts as a rarer medium than the air upwards. A ray of light coming from the top of the tree passes from denser layers to rarer layers and undergoes total internal reflection to the observer. Due to the total internal reflection of light, the observer feels an illusion that there would be water on the road and floating the tree on it. This is mirage.
The sparkling of diamond is due to the total internal reflection of light. Since, the critical angle of diamond is very small (i.e. 240), the light entering in a diamond undergoes multiple total internal reflections and light gets trapped in it. This causes sparkling of diamond.
1. Light pipe or optical fibers work on the principle of total internal reflection.
2. It is used to construct instruments like binoculars.
A light pipe is a bent rod made by transparent glass which works on total internal reflection of light.
It is used by the doctors to observe the internal organs like stomach, nose, ear, etc.
Solution:
The relation is given by,
Refractive index (µ) =
Here,
Real depth = 3m
Refractive index = 1.33
Apparent depth = ?
We know,
RI (µ) =
or, 1.33 =
or, Apparent depth = 3/1.33
∴ Apparent depth = 2.256m.
Solution:
Here,
Real depth = ?
Refractive index =
Apparent depth = 5m
We know,
RI (µ) =
or, =
or, real depth = 20/3
∴ real depth = 6.66m
Solution:
Here,
Angle of incidence (∠i) = 300
Angle of refraction (∠r) = ?
Refractive index (µ) = 1.5 We have,
Refractive index =
or, 1.5 =
or, Sin r =
or, Sin r = 1/3
or, r = Sin-1 (1/3)
∴ r = 19.470
Hence, the angle of refraction is 19.470
Angle of incidence (∠i) = 450
Angle of refraction (∠r) = 300
Refractive index (µ) = ?
We have,
Refractive index = = = = = 1.414
Hence, refractive index of the ice is 1.414.
Solution:
Here,
Real depth = 20cm
Refractive index (µ) = 1.33
Apparent depth = ?
We know,
Refractive index (µ) =
or, 1.33 =
or, Apparent depth = 20/1.33
∴ Apparent depth = 15.03 cm

Solution:
Here,
Speed of light in air (c) = 3 x 108 m/s
Speed of light in glass (v) = 2 x 108 m/s
RI of glass (µ) = ?
Now,
µ = = = 1.5

Solution:
Here,
Speed of light in air (c) = 3 x10 $^{8}$ m/s
Speed of light in diamond (v) =?
RI of diamond(µ) = 2.42
Now,
µ =
or, v =
or, v =
or, v = 1.24 x 108 m/s
Hence, the speed of light in diamond is 1.24 x10 $^{8}$ m/s.

Here,
Angle of incidence (i) = 20$^{0}$
Refractive index of glass (µ) = 1.5
Angle of refraction (r) = ?

We know that ,
µ = $\frac{sin\;i}{sin\;r}$
1.5 = $\frac{sin\;20}{sin\;r}$
sin r = $\frac{sin\;20}{1.5}$
or, r = sin $^{-1}$ $\frac{0.3420}{1.5}$ = 13.18 $^{o}$

Therefore, the angle of refraction in glass is13.18 $^{o}$

Here, Real depth = 2m
R.I. of water = 1.33
Apparent depth = ?
We have,
R.I. = $\frac{Real\;Depth}{Apparent\;depth}$
or, 1.33 = $\frac{2}{Apparent\;Depth}$ = 1.503 m
$\therefore$ Apparent Depth of the pond is 1.503 m.

Here ,
Refractive index of diamond (µ) = 2.42
Critical angle (C) = ?

We know ,
$\therefore$
SinC = $\frac{}1{µ}$
or, C = $sin^{-1}$ ( $\frac{1}{2.42}$ ) = 24.41 $^0$C

Therefore, the critical angle of diamond is 24.41 $^0$C .

Here,
Resistance (R) = 2Ω
Current (I) = 2A
Potential Difference = ?

From, Ohm's law, we have
V = IR
V = 2 $\times$ 2
$\therefore$ V = 4V

Hence , the potential difference is 4V.

Diameter (d) = 0.44 $\times$ $10^{-4}$m
Resistance (R) = 10Ω
Resistivity (ρ) = 4.43 $\times$ $10^{-7}$ Ωm
Length (l) = ?
We know,
R = ρ $\frac{1}{A}$
or, R = ρ $\frac{1}{πd^2}$ $\times$4
10 = $\frac{4.43 \times 10^{-7} \times l \times 4}{\frac {22}{7} 4.4 \times 10^{-4} \times 4.4 \times 10^{-4} }$
l = $\frac{10 \times 22 \times 4.4 \times 4.4 \times 10^{-8} }{7 \times 4.43 \times 4 \times 10^ {-7} }$
or, l = $\frac{4.26 \times 10^{-5}}{1.24 \times 10^{-5} }$
= 3.42

Hence, the length of the manganin wire is 3.42 m.