Download INDIRECT METHODS FOR MEASUREMENT OF DISTANCE

MEASUREMENT OF DISTANCE XI CLASS
ALFA PHYSICS CLASSES
INDIRECT METHODS FOR MEASUREMENT OF DISTANCE
[1] Echo Method: This method is used to find the distance of far object like a hill. To measure
this distance a gun is fired and time interval is noted between the instant of firing and the
instant echo is heard. This is the time in which the sound travel distance from observer to hill
and back. If S is distance between observer and hill then in this time t sound travels a
distance 2S.
2S = vt
S=
vt
2
Where v is the velocity of sound waves.
The same concept can be used in measuring the distance between say
moon and earth. LASER is used in place of sound waves. The LASER beam is send towards
moon, if the beam returns to observer after time t then in this time the beam has covered a
distance equal to 2S, where S is distance between earth and moon
S=
ct
2
Where c is the velocity of light or LASER beam.
[2]SONAR Method: In Sound Navigation and Ranging ultrasonic waves are used to measure
distance of under water objects like submarines or rocks also. The ultrasonic waves from the
transmitter are sent through the water. If a submarine comes in the path these waves are
reflected back and comes back to transmitter. The time interval is measured between instant
the waves are send and the time they are received. If this time is t then the distance of
submarine is
S=
vt
2
Same method can be used in RADAR where radio waves are sent towards an aeroplane. If
after reflection they are received by the radar we can measure the distance of aeroplane
from time taken by wave for to and fro journey.
Triangulation Method: This method is used to measure the height of building.
Direct Method: This method is used where the distance of the base of the building from the
observer is known. We measure the angle which the given tower AB makes at the
observation point. It is called elevation of the tower at P.
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Res: 86, Chotti Baradari Part-1, Near Medical College, Jalandhar #98152-15362
MEASUREMENT OF DISTANCE XI CLASS
ALFA PHYSICS CLASSES
Tan θ =
h
x
H = x tan θ
Thus if we know the distance x we can find the height of the tower.
Indirect Method: Sometimes the distance of the tower from the observation
point is not known then we use indirect method for measurement of height of the tower. We
use two different points to measure the elevation of the tower. The distance between these
two observation points is called basis. As shown in figure .
Cot θ1=
Cot θ2=
P1 A
h
P1 A  x
h
Cotθ2- Cotθ1=
h=
x
h
x
cot  2  cot 1
If we know the value of basis, θ1 and θ2 we can find the height of the tower.
To measure the size of an astronomical object: let moon be the astronomical
object whose diameter is to be found. For this let E be the observation point on
the earth and a telescope is focused on the surface of the moon and its disc
image is observed. Using telescope we measure the angle subtended by the two
opposite ends of the diameter of the moon on the surface of earth. If this angle is
θ, then
Θ=
length of arc D

radius
S
Knowing the distance S between earth and moon and the angle θ we can find the diameter
of the earth. This formula will hold if S is very large and diameter of the moon can be
considered a small arc.
Parallax Method: The shift in the position of the image due to the shift in observation point
for seeing the object is known as parallax. The distance between the two observation point is
called the basis.
For e.g. if we hold an object in front of the eye against a background wall its image formed
changes position when seen by the right eye and when seen by the left eye. This is called
parallax and distance between two eyes is called basis.
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Res: 86, Chotti Baradari Part-1, Near Medical College, Jalandhar #98152-15362
MEASUREMENT OF DISTANCE XI CLASS
ALFA PHYSICS CLASSES
The parallax method has been used for measuring distance of starts which
are less than hundred light years away. The diameter AB of earth’s orbit around
the sun is taken as the basis. N is the nearby star whose distance is to be measured
and F is another star which is very far away and its position relatively remains
unchanged relative to earth. We measure the angle between light coming from
the two stars F and N at two diametrically opposite positions of earth in its motion around
sun. Let the two angles measured be θ1 and θ2, then the angle wheich nearby star subtends
at the orbital diameter of earth is θ1 + θ2.
Θ 1 + θ2 =
AN =
AB
AN
AB
1   2
Here AB is equal to 2AU=3x1011m, thus if we know the value of θ1 +θ2, we can find the
distance of the star.
Note: Parallax method can also be used to measure the diameter of moon. To places which
are far removed from each other form the base line. Using astronomical telescope we
measure the parallax angle and thus the diameter of the moon.
Size of Oleic acid Molecule:
Small distances can be measured directly using variety of devices like screw gauge, Vernier
Calipers, microscope etc. But some indirect methods are also there. For example, to
estimate the size of molecule take 1 c.c. of oleic acid and dissolve it in 20 c.c. of alcohol and
more alcohol is added to increase the volume to 30 c.c. The final solution is 1/30 c.c. of oleic
acid in 30 c.c. solution and its concentration is 1/900 c.c. of oleic acid in 1 c.c solution. Put
n drops of this solution carefully on the surface of water in the vessel. Stretch out this film
on the surface of water and in the mean time measure the volume of 100 drops and from
there find volume of 1 drop. Let it be V. In volume V, the volume of oleic acid is V/900 c.c.
and in n drops volume of oleic acid is nv/900 c.c. When the alcohol has evaporated only
oleic acid remains spread on the surface of water in the form of thin film. Assume that the
film has thickness of the size of molecule. Measure the area of film, let it be a. Then,
nv
900
nv
x 
900a
xa 
Thus, x or size of oleic acid molecule can be measured.
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Res: 86, Chotti Baradari Part-1, Near Medical College, Jalandhar #98152-15362