Note on Causes of Refraction of Light

  • Note
  • Things to remember
  • Videos
  • Exercise
  • Quiz

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.

  • 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.
.

Very Short Questions

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.

0%
  • Refraction occurs when

    when light passes through two objects
    when light passes through two air mediums
    when light passes through two mediums
    when light passes through different optical medium
  • Refraction occurs due to

    Difference in optical conductance in two optical medium
    Difference in speed of light in two optical mediums
    Difference in optical luminosity in two optical medium
    Difference in optical transparency in two medium
  • Which is not law of Refraction?

    when light ray travels from a rarer to a denser medium, it bends towards normal
    the incident ray, refracted ray and the normal all lie on same point on the different plane
    when light ray travels from a denser to a rarer medium, it bends away from normal
    ray of light which hits perpendicular to the surface separating two media passes undeviated
  • What does aug denote?

    Ratio of refractive index between glass and air
    Ratio of Refractive index between air and glass
    Refractive index of air with respect to glass
    Refractive index of glass with respect to air
  • The refractive index of Alcohol is 1.31, of glass is 1.5, of benzene is 1.5 sand of diamond is 2.42. It means that?

    Benzene is more volatile than Alcohol
    Speed of light in both glass and benzene are same
    Alcohol is liquid and Diamond is solid
    Diamond is harder than glass
  • Twinkling of stars is due to

    Refraction across different air particles in atmoshpere
    Refraction across different layers in atmoshpere
    Passage of light across different layers of hot and cold air in atmoshpere
    Refraction across different air layers in atmoshpere
  • What is a prism?

    A transparent reflecting medium bounded by two plane surfaces inclined at some angle
    A transparent refracting medium bounded by 6 plane surfaces inclined at some angle
    A transparent refracting medium bounded by two plane surfaces inclined at parallel angle
    A transparent refracting medium bounded by two plane surfaces inclined at some angle
  • What is requirement for total internal reflection?

    Incident angle must be greater than critical angle as ray passes from rarer to denser medium
    Incident angle must be greater than critical angle as ray passes from denser to rarer medium
    Critical angle must be larger than incident angle as ray passes from denser to rarer medium
    Light must reflect back to the same medium as ray passes from denser to rarer medium
  • The sparkling of Diamond is not a result of it's

    Total internal reflection
    Smoothness
    refractive index is very low
    many steep faces
  • Why glass is not as shiny as Diamond?

    It's texture is not as smooth as diamond
    It's critical angle is higher than diamond
    It is less hard than diamond
    It is more brittle than diamond
  • Which is not an effect of total internal reflection?

    Looking over the wall with a periscope
    Twinkle of stars
    Seeing image of water in a hot desert
    Diamond sparkle
  • You scored /11


    Take test again

DISCUSSIONS ABOUT THIS NOTE

You must login to reply

Forum Time Replies Report
nishan

if fish in aquarium is observed from the bottom it appears in air


You must login to reply

Astin

What is critical angle and total internal reflection


You must login to reply

avisek passone

if a spear is shot exactly at the place where fish is seen in water , the fish does not get heat.


You must login to reply

rohit

Why sky appear blue and space appear black


You must login to reply