Recents in Beach

Measurement of micro and large distances. Parallax Method | diameter of the moon echo method or reflection method

(A) Measurement of micro and large distances:

 Here we will study about two types of distances, first when the distance is very small (less) and second when the distance is very large.  We will also find out here how and by what methods it is possible to measure them.

 Special methods and methods are used to measure very small distances, if they are included in very small distances, then there is a very small distance such as the size of the atom, the diameter of the molecule etc.

The distance of 10-6 m  range is measured with the help of optical microscope.

The distance of 10-8m  range is measured with the help of electron microscope.

 Here we will study the method of calculating the diameter of any molecule, how we can calculate the diameter of a molecule.

 Here we will calculate the diameter of the molecule of oleic acid.  In this method, we will create a thin layer of oleic acid on the surface of water and assume that the thickness of the layer of oleic acid is equal to the diameter of the oleic acid.
 First of all dissolve oleic acid of 1 cm3 volume in 20 cm3.
 After mixing it well, 1 cm3 volume is taken from this solution and this 1 cm3 volume is taken again.
 dissolve in alcohol of 20 cm3 volume.
 The concentration of the solution thus formed will be (1/(20×20)) cm3 .
 n drops of this solution are put on a flat surface of water and these droplets are spread well on the surface of the water, on keeping it in the open the alcohol evaporates and leaves behind a layer of oleic acid.
 Now we measure the area of ​​the layer of this oleic acid by graph method or any other method.
 Let us assume that the volume of n drops is nV.
 Thus, volume of oleic acid =  nV x (1/(20×20))
 We know that Volume (volume of solution) = Area x Thickness of film
 Volume (V) = At
                At  = nV x (1/(20×20))

                 t  = nv /400A

 Since we had initially assumed that the thickness of the layer of oleic acid is equal to the diameter of its molecule.  Therefore, the thickness (t) of the oleic acid layer obtained here is equal to the diameter of the molecule.

(i) Atomic size calculation or Avogadro method:- We cannot use the volume of a substance to find the volume of an atom, because there is some empty space between the atoms present in the substance, due to which we cannot find the actual value of the volume of atoms present in it by the substance.

 Therefore Avogadro's use is used to find the size (volume) of an atom, as it gives the actual value of the atom's volume.

On this basis, the following formula is given to find the value of the radius of an atom in this method.


 Here r = Radius of the atom

 N = Avogadro number

 p = density of the substance


(B) measurement of large distances

 We have studied above about the methods of measurement of subtle distances, now we talk about if the distance is of a very large range, such as the distance between the moon and the earth, and the distance of stars etc.

 Special methods are also used for the measurement of such distances because these distances cannot be measured with any scale.

We will study here some of the methods used to measure these huge distances, which are as follows –


(i) Parallax method or Displacement method

 Before reading the parallax method, we first understand what is parallax?

 Parallax: If we see an object placed in front of us with both eyes, we often see with one eye closed and the other eye with the first eye, then we find that the object appears to be displaced somewhat relative to some axis, this effect  It is called Kolamban.
 That is, when the pencil placed in front of us is seen with the right eye with the left eye closed relative to a center, then the dye is seen with the left eye by closing the eye, then we find that the position of the pencil is somewhat deviated relative to the center point.  This effect is called the parallax effect.  We use the same effect in the parallax method.  But here we study its position by looking at a star from two different positions at the same time, not by looking with the eye.

As shown in the figure, the star (S) is seen from two different positions A and B, when s star is seen at the same time, an angle is formed between them which is shown as it is called parallax angle.
 The distance between A and B is b and the distance between A to S and B to S is D.
 by the rule of triangles
         
       = AB/D
      = b/D
     D = b/θ
 Here is measured in radians, the distance (D) of the star from the earth can be calculated by keeping the value of in radians.

(ii) Size of celestial body or diameter of moon (size of astronomical object : diameter of moon in hindi ):

 We cannot measure the size of any celestial body with our eyes, there can be many reasons for this like we are situated at a very long distance, many mediums come in the middle etc.

 To find the size (diameter) of a celestial body like the moon, we use the parallax method.

 According to the picture, we see the moon from the earth, telescope is used to see, when the moon is seen from the telescope it looks like a circular shape as shown in the picture.

 The angle subtended by α is formed by both the ends of the moon, the distance of the moon from the earth is shown by S.

 If α is taken in radians and distance (s) is taken in metres, then the diameter (D) of the moon is given as -

 Diameter (D) = Sα


(iii) Resonance method or reflection method for measurement of large distances

 It is often used by the Navy or ships, when the ships move at night, they are not able to see the distant hill, so the echo method is used to locate the distant hill and find its distance from the ship.  is done.

 In this method a shot is fired from the gun in the front of the ship, if there is a mountain in front, the sound comes back after hitting the mountain, in which case the bullet is fired and the moments between the sound return are noted and  The distance to the hill in front is ascertained at the base.

 Let sound is moving with velocity V and time interval t is obtained, then the distance of the hill is s.

 Total distance traveled by sound to the hill and back to the ship = s + s = 2S

 So 2S = vt

 Thus, distance (S) = vt/2