Physics - Chapter Three| Mirage
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Physics - Chapter Three| Mirage
It is a natural phenomenon observed on hot days,
responsible for the wet appearance of paved roads in
summer and the illusion of seeing water in deserts
The mirage can be explained as follows:
1-On very hot days, the air layers above the ground get hotter (optically
lesser dense) (lower refractive index) than the upper layers
2-As a light ray from an object (e.g. the sky or a palm tree) travels from
the upper layers (denser) to the lower ones, it refracts away from the
normal, and keeps deviating taking a curved path.
3- Accordingly, the angle of incidence increases from a layer to another.
4-When the angle of incidence becomes more than the critical angle,
it undergoes total internal reflection and the ray is curved up.
5-When the ray reaches the observer's eye, it seems reflected from water
surface. An inverted image is seen below the object.
The occurrence of mirage in deserts.
Due to high temperature in deserts, the air layers adjacent to the surface of the Earth are heated, their density and refractive index decreases.
If we follow a light ray reflected off a palm tree, this ray refracts away from the normal, and keeps deviating taking a curved path.
When its angle of incidence reaches more than the critical
angle, it undergoes total reflection and the curve goes up.
Scientific Basic of Mirage:
Total Internal Reflection When the angle of incidence in denser
medium is greater than the critical angle, the ray is totally reflected
Deviation of Light through a Triangular Prism:
When a light ray is incident on one side of a triangular prism, it may refract twice emerging towards the prism base.
Because of this, the image of an object is seen through the prism displaced towards the prism vertex.
Equilateral triangular prism: Is used in deviation & dispersion of white light.
is the angle of incidence on the first surface.
is the angle of refraction on the first surface.
is the angle of incidence on the second surface.
is the angle of emergence.
A is the refractive angle of the prism.
is the angle of deviation.
The geometry of the figure shows that:
Thus,
Angle of deviation : Is the acute angle between the produced extensions
of the incident ray and the emergent ray.
Factors affecting on angle of deviation angle in a triangular prism ( )
1-Angle of incidence
2-Refractive angle of the prism ( A)
3-Refractive index of the prism material ( n)
* For light of a certain wavelength passing through the same prism,
Angle of deviation depends upon the angle of incidence
* The practical study for this relationship showed that:
- At small angles of incidence, as increases, decreases.
- until reaches a minimum value called minimum
angle of deviation at a certain angle of incidence
This is the position of minimum deviation
- When angle of incidence exceeds , increases
- At the position of minimum deviation:
and
Snell’s law could be written as:
Notes:
* In a triangular prism, as the angle of incidence increases:
The angle of refraction increases.
The angle of the second incidence decreases.
The angle of emergence decreases.
* The smallest angle of incidence that causes the ray to emerge through
the opposite side:
* As angle of minimum deviation increases, the refractive index increases.
Examples:
1-A light ray is incident normal to one face of a triangular prism of angle
480 The ray emerges tangent to the other face.
Calculate refractive index of the prism.
Solution:
2-In equilateral triangular prism, a light ray falls on one face of the prism
by angle 300 , follow its path and determine the angle of emergence if
refractive index of prism is 1.5
Solution:
3-A triangular prism of refractive angle 60°, adjusted to the minimum deviation position, when the angle of minimum deviation is 3 7.2°.
Find its refractive index.
Solution:
Experiment to determine the ray path through a glass prism and its
refractive index:
Tools:
An equilateral triangular prism (A = 60°), pins, a protractor, a ruler.
Procedure:
1) Place the glass prism on a sheet of drawing paper with its surface in a
vertical position and mark its position with a fine pencil line.
Place two pins such that one of them (a) is very close to one side and the
other (b) is about 10 cm from the first.
The line joining them represents the incident ray.
Look at the other side of the prism to see the image of the two pins,
one behind the other, Place two other pins (c) & (d) between the prism
and the eye such that they appear to be in line with the 2 pins (a) & (b)
i.e., the four pins appear to be in one straight line.
Locate the positions of the four pins
2) Remove the prism and the pins, join (b) and (c) to locate the path of the
ray (a b c d) from air to glass to air again.
3) Extend dc to meet extended (ab).
The angle between them is the angle of deviation ( )
4) Measure the angle of incidence ( ), the angle of refraction ( ),
the inner incidence angle ( ), the angle of emergence ( ) & the angle
of deviation
5) Repeat the previous steps several times changing the angle of incidence
and tabulate the results.
Angle of the
prism A angle of
incidence
angle of
refraction
Angle of inner
incidence
angle of
emergence
Angle of
deviation
Find the minimum angle of deviation and the corresponding angles ( ) and) )
- Then obtain the refractive index from equation
The dispersion of light by a triangular prism:
The refractive index (n) depends on up the wavelength then the minimum angle of deviation depends also on the wavelength.
Thus, if a beam of white light falls on a prism set at the minimum angle of deviation, then the emerging light disperses into spectral colors.
It is concluded that the violet ray has the largest deviation (maximum refractive index).
The visible spectral colours into which the white
light is dispersed are arranged by the order:
red, orange, yellow, green, blue, indigo and violet.
The prism disperses white light to its seven colours.
Because the wavelength of each colour is different than the other and the refractive index depend on the wavelength so each one has its own deviation.
The rectangular glass block doesn't disperse white light to its seven colors.
Because the rectangular glass block is considered as two equals opposite prisms from the same material, the dispersion of the first prism is cancelled by the second.
The red colour has the minimum deviation, while violet light has maximum deviation in a prism.
Because the red light has maximum wavelength so it has minimum deviation while the violet light has minimum wavelength and maximum deviation.
The thin prism:
A thin prism is a triangular glass prism.
Its apex angle is a few degrees and is in the position of minimum deviation.
and are small angles.
(radians)
And (radians)
Application:
The thin prism: It is used in deviation and dispersion of white light.
Examples:
A thin prism of refractive index 1.5 is placed in a liquid of refractive index 1.2 has angle of deviation 2°. Find the angle of prism.
Solution:
Dispersive Power:
When white light falls on a prism, the light disperses into its spectrum due to the variation of the refractive index with wavelength.
where nr is the refractive index for red and for blue.
By subtracting,
The LHS represents the angular dispersion between blue and red.
For yellow (middle between blue and red), the angle is:
where is the refractive index for yellow.
If is the average of and then is the average of and We define as
where is the dispersive power, and is independent of the apex angle.
Angular size (dispersion): Is the angle between the deviation angle of blue
and red rays after emergence from prism
Dispersive power ( ): Is the ratio between the angular size to the
deviation angle of the yellow light.
Factors affecting on angular size of a prism:
1-Deviation angle for blue ( )
2-Deviation angle for red ( )
Factors affecting on dispersive power of a prism ( )
1-Angular size of spectrum ( angular size)
2-Mean deviation angle
Graphs:
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