Refraction through triangular prism,
Real and apparent depth,
Total internal reflection and its application
Refraction Through Triangular Prism
When a ray of light passes through a triangular prism, it is refracted as shown below
The angle between the incident ray and the emergent ray is known as the angle of deviation. The angle of deviation decreases as the angle of incidence increases
Refraction is change in direction of light rays. Refraction occurs whenever light rays travel from a transparent medium to another transparent medium of different density.
The abrupt change in direction at the surface of the two media is referred to as refraction. Refraction occurs when light travels from air to glass or from air to liquid in two different media is responsible for refraction or bending of light rays. It is important to define some of the parameters associated with refraction of light.
The incident ray (AO) is the path along which the light travels in the first medium
The refracted ray (OB) is the path along which the light travels in the second medium
The angle of incident, i, is the angle between the incident ray and normal to the surface at O.
The angle of refraction, r, is the angle between the refracted ray and the normal to the surface at O.
The refractive index,
https://youtu.be/-YavkGfZFR4
TERMS ASSOCIATED WITH REFRACTION
(i) The incident ray: This is the direction of rays of the light from the source to the first medium.
(ii) The refracted ray: This is the direction to with the light travels from the point of incidence to the second medium which is always denser than the first medium.
(iii) The angle of incidence: This is the angle at which the incident ray mixes with the normal in the first medium.
(iv) The angle of refraction: This is the angle at which the refracted ray mixes with the normal in the second medium.
REFRACTIVE INDEX FROM A DENSER MEDIUM TO A LESS DENSE MEDIUM
If refraction occurs from a dence medium to a less dense medium, e.g glass to air, the refractive index µ is equal to
µ= fµa = 1/aµg
if it from water to air,
µ= wµa = 1/aµw
A ray of light could be produced from a denser medium to a less dense medium or from a less dense medium to a denser medium. The refractive index from glass to water is given below
gµw = 1/wµg
REFRACTIVE INDEX (µ)
Refractive index is a constant used to express the nature of medium through which light ray is propagated. The refractive index determines the extent of permeability at which ray travels through a medium. The ratio of sin i to sin r which is equal to a constant is known as the refractive index µ. This can also be defined as the nature of the material which medium is made of. Sometimes it is defined in relation to the extent at which a medium allows light ray to pass through it.
Refractive index can be determined mathematically by bringing into consideration the various factors that change, i.e, wavelength µ, velocity V, and the direction during the process of refraction.
Mathematically, refractive index is denoted by µ and is given as:
µ = sin i/ sinr ...................................(i)
µ = VA/VB = λA/λ B = Velocity of A / velocity of B – wavelength A/ wavelength B
µ = Real depth /Apparent depth .....................................(iii)
Example 1: A ray of light is incidented in water at an angle of 200, from water to glass plane surface. Calculate the angle of refraction in the glass aµg = 1.5, aµw = 1.33 = 4/3 .
Solution
gµw = aµw/ gµa
gµa = 1/aµg = 1/1.5 = 2/3
gµw = 4/3 = 8/9 = 0.8889
2/3
wµg = sin i / sinr = sin 200/ sin r
0.8889 = sin20/sinr
0.8889 x sin r = sin 20
Sin r = sin 20/0.8889 = 0.3420/0.8889
Sin r = 0.3847
r = sin -1 (0.3847)
r = 22.62
r = 230
https://youtu.be/4l2thi5_84o
TOTAL INTERNAL REFLECTION
When light passes at a small angle of incidence from a denser to a less dense medium e.g. from glass to air, there is a strong refracted ray. There is also a weak ray reflected back into the denser medium.
When the angle of incidence increases, the angle of refraction also increases. At a certain increase of the angle of incidence, the angle of refraction is 90º. This angle of incidence in the denser medium for which the angle of refraction in the less dense medium is 90º, is referred to as the critical angle ( c). For angle of incidence greater than C, the refracted ray disappears and all the incident light is reflected back into the denser medium. At this point, the ray is said to experience total internal reflection. Example of total internal reflection is the mirage on the road, where the refractive density of warm air is less than that of cool air and light meets a layer at a critical angle, it suffers total internal reflection.
https://youtu.be/T-iy29oEmSI
REAL AND APPARENT DEPTH
A thick slab of glass appears to be only two –third of its real thickness when viewed vertically from above. Similarly, water in a pond appears to be only three quarters of its real depth. Rays from a coin at the bottom of a bucket of water are refracted away when they leave water and enter the eyes. They appear as if coming from a virtual image, which is apparent depth while the actual depth of the bottom remains and is referred to as real depth.
Refractive index=[sup]real depth[/sup]/[sub]apparent depth[/sub]
https://youtu.be/30FCqf46TK8
REFRACTIVE INDEX OF LIGHT
PRACTICAL APPLICATION OF REFRACTIVE INDEX
(i) To confirm the identity of a substance, refractive index may be employed.
(ii) In removing chromatic aberration by using a double lenses made of materials of different refractive indices.
(iii) In analysis mixtures, a refractive index may be employed.
Example 1: A coin is placed at the bottom of a pond, 3m deep. Calculate the apparent displacement of the coin when it is viewed directly from top ( µ of air to water = 4/3 )
Solution
µ = Real depth/ Apparent depth
Apparent depth = Real depth /µ
µ = 3 = 3/1 x ¾
4/3
µ = 9/4 = 2.25
Apparent depth = 2.25
CRITICAL ANGLE
Critical angle is the angle of incidence in the denser medium when the angle of refraction in the less dense medium is 90º. It is denoted by C
fig : 2.1 Critical angle
The refractive index of air to glass = sin i/sin r
Since sin i = sin r = 90º
aµg = sin 90 /sinc , sin 90 = 1
aµg = 1/sinc.
TOTAL INTERNAL REFLECTION
When a ray of light passes from optically denser medium to optically less dense medium, there exist a weak internal reflection and a strong refraction. But as the angle of incidence increases, the angle of refraction also increases and at the same time, the intensity of the reflected ray gets stronger and that of the refracted ray becomes weaker.
When the angle of incidence exceeds the critical angle, there exists no refraction and a total reflection occurs, This phenomenon is called total internal reflection.
Fig : 2.4 Total internal reflection
The conditions under which total internal reflection occurs are:
(i) Light rays must travel through a denser medium to a less dense medium.
(ii) The angle of incidence must exceed critical angle.
APPLICATION OF TOTAL INTERNAL REFLECTION
The principle of total internal reflecting is adopted i the invention and operation of the following:
(i) Binoculars
(ii) Mirage
(iii) Refractometer
(iv) Optical fibres
(v) Total reflecting prisms are employed in periscopes, prism binoculars, projection lanterns and cameras,
(vi) Total internal reflection of radio waves is employed.
https://youtu.be/T-iy29oEmSI
OPTICAL FIBRES
Optical fibres have two parallel plane mirrors covering a transparent glass. The density of the transparent glass and the refractive index is greater than the density of two mirrors and because of this the glass itself can totally and internally reflect rays from the object itself.
Optical fibres are used (i) in conveying information (ii) in medical laboratory to see deep down the throat of a patient.
https://youtu.be/rS-zUcAOFd0
MIRAGE
Temperature is a major determinant of mirage. The degree of hotness or coldness of a body varies from place to place. The temperature in the desert is different from that in the rain forest.
To driver, driving on a road in a temperature region on a good sunny day, it could mean that the air very close to the ground is hot and in which the hotter air is optically less dense.
Rays from the sky passing through the cold air, on getting to the normal air layer bends easily from the incident direction into the layer of the air very close to the ground. At a point, water appears to the driver is like a pool of water in his front and anything placed beside it seems inverted.
https://youtu.be/pMMJo2q5ADM
REFRACTION THROUGH PRISM
There are two types of prisms namely;
(i) Rectangular prism
(ii) Triangular prism
Rays are produced from rectangular prism which has the angle of refraction either produced from the normal or produced to the normal, but rays transmitted through a triangular prism are always refracted towards the normal and close to the base of the triangular prism.
(i) The angle of incidence, i
(ii) Angle of refraction, r
(iii) Angle of emergence, e
(iv) Minimum deviation, dm
(v) Equilateral angle, A
A = 60º, IF THE PRISM IS EQUILATERAL.
General Revision
1. Distinguish between the resultant and equilibrant forces.
2. Give two (02) ways to increase the stability of a body.
ASSIGNMENT
1. The direction of a light ray changes as it passes from one medium to another. This phenomenon is called A diffraction B reflection C dispersion D refraction
2. The velocities of light in air and glass are 3.0 x108 m/s and 1.8 x108 m/s respectively. Calculate the sine of the angle of incidence that will produce an angle of refraction of 300 for a ray of light incident on glass A 1.2 B 1.0 C 0.8 D 0.6
3. A transparent rectangular block 5.0 cm thick is placed on a black dot. The dot when viewed from above is seen 3.0 cm from the top of the block. Calculate the refractive index of the material of the block A 2/5 B 3/5 C 3/2 D 5/3 E 5/2
4. When a ray of sunlight passes obliquely through a rectangular glass block
Ait emerges without displacement parallel to the incident ray
B it gets dispersed into seven visible colours without any deviation at all
C it deviates without dispersion
D it gets laterally displaced and the emergent ray is parallel to the incident ray
5. The absolute refractive indexes of glass and water are 3/2 and 4/3 respectively. The refractive at the interface when a ray travels from water to glass is
(A) ½ (B) 8/9 (C) 9/8 (D)17/12
THEORY
1. A ray of light passes from air through a rectangular block of glass with parallel side 4.5 cm apart at an angle of incidence of 52º,find
A The lateral displacement of the ray B The angle of refraction (Refractive index of glass=1.5)
2. The critical angle for a transparent is 39. Calculate the refractive index of the substance.
New school physics for senior secondary school pages 266-270
