Today, we will learn about the simple and compound microscopes, which are related to Class 12 physics.
Simple Microscope
A simple microscope consists of a convex lens with a short focal length. It is an optical device used to obtain magnification of small objects of better clarity of vision.
Simple Microscope
A simple microscope consists of a convex lens with a short focal length. It is an optical device used to obtain magnification of small objects of better clarity of vision.
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| Simple Microscope |
Principal
To obtain a larger image of the object, the object is placed between the focus and the pole. This gives a large virtual, and erect image of the object.
Diagram of A Simple Microscope
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| Simple Microscope Ray Diagram |
Magnification
Magnifying Power: Magnifying power of a microscope is defined as the ratio of the angle subtended by the final image at the eye and the angle subtended by the extended object placed at least the distance of distinct vision.
Linear Magnification
Linear magnification refers to the ratio of image length to object length measured in planes that are perpendicular to the optical axis.
A negative value of linear magnification denotes an inverted image.
`M = \frac{\beta}{\alpha}`
`M = \frac{tan\beta}{tan\alpha}` {For small angle}
`M = \frac{(\frac{AB}{OB})}{(\frac{AB}{OB'})}`
`M = \frac {AB}{OB} \times \frac {OB'}{AB}`
`M = \frac {OB'}{OB}`
`M = \frac {- D}{- u}`
`M = \frac { D }{ u }` ....... eq. 1
Case I
When an image is formed at least the distance of the distinct vision
Lens formula
`\frac{1}{f} = \frac{1}{v} - \frac{1}{u}`
Here
u = - u and v = - D
`\frac {1}{f} = \frac{1}{- D} - \frac {1}{- u}`
`\frac {1}{f} = \frac{1}{u} - \frac {1}{D}`
On multiplying both sides by D
`\frac {D}{f} = \frac{D}{u} - \frac {D}{D}`
`\frac {D}{f} = M - 1` {`\because \frac {D}{u} = M`}
` M = 1 +\frac {D}{f}` ....... eq. 2
This is the maximum magnifying power
Case II
When the image is obtained at infinity
When the object is placed at the point of focus, the image is obtained at infinity.
Thus u = f
from equation 1
`M = \frac { D }{ f }`
This is the minimum magnifying power
Use of a Simple Microscope
- An astrologer uses a simple microscope to see the lines of the palm. (Palmists generally use a magnifying glass while seeing palm lines.)
- In the laboratory of science, a microscope is used to obtain the readings of the vernier caliper, screw gauge, etc.
- The parts of a wristwatch are very small, the watchmaker uses a simple microscope to see them.
- An astrologer uses a simple microscope to see the lines of the palm. (Palmists generally use a magnifying glass while seeing palm lines.)
- In the laboratory of science, a microscope is used to obtain the readings of the vernier caliper, screw gauge, etc.
- The parts of a wristwatch are very small, the watchmaker uses a simple microscope to see them.
Compound Microscope
Construction
In this, there is a convex lens of short focal length and small aperture, which is placed towards the object; it is called the object lens or field lens. The second convex lens is of larger focal length and large aperture, and it is placed towards the eye; it is called the eye lens.
Both these lenses are arranged on the sides of a metal tube, the distance between these lenses can be increased or decreased by a wheel arrangement.
Adjustment and Formation of Image
In the adjustment process, the eye lens or eye pieces are adjusted first. For this, eye eyepiece is moved forward or backward up to such an extent that the cross wire should be seen clearly.
Now the object is placed in front of the field lens, and it is moved to adjust in such a way that the clear image of the object is seen. In this situation inverted larger and virtual image of the object forms on the cross wire.
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| Compound Microscope |
AB is a small object, and its inverted, real, and larger image A'B' is formed by the objective lens. This image acts as a virtual object for the eye lens; therefore, it is moved forward or backward such that the image A'B' may lie within the focal length `f_e` of the eyepiece.
The image A'B' acts as an object for the eyepiece, which essentially acts like a simple microscope. The eyepiece forms a virtual and magnified final image A'' B'' of the object clearly, and the final image is inverted to the object AB.
Magnifying Power
`M = \frac {\beta}{\alpha}`
`M = \frac {tan\beta}{tan\alpha}`
`M = \frac {\frac{A'B'}{EB'}}{\frac{AB}{EB}}`
`M = \frac{A'B'}{EB'}\times\frac{EB}{AB}`
`M = \frac{A'B'}{AB}\times\frac{EB}{EB'}`
`M = \frac{OB'}{OB}\times\frac{EB}{EB'}``[\because \frac{A'B'}{AB}=\frac{OB'}{OB}]`
`M = \frac{v_o}{- u_o}\times\frac{- D}{-u_e}`
`M = - \frac{v_o}{ u_o}\times\frac{D}{u_e}` .....eq(1)
`M = m_o m_e` ........(2)
Case I
If the final image formed at least a distance of distinct vision
then `v_e = - D`
lens formula
`\frac{1}{f}=\frac{1}{v} - \frac{1}{u}`
`\frac{1}{f_e}=\frac{1}{-D} - \frac{1}{- u_e}`
`\frac{1}{f_e}=\frac{1}{-D} + \frac{1}{u_e}`
`\frac{1}{u_e}=\frac{1}{D} + \frac{1}{f_e}`
Multiply by D on both sides
`\frac{D}{u_e}=\frac{D}{D} + \frac{D}{f_e}`
`\frac{D}{u_e}= 1 + \frac{D}{f_e}`
From eq (1)
`M = - \frac{v_o}{ u_o} (1 + \frac{D}{f_e})` ....eq(3)
Case II
If the final image formed at infinity
In this condition, `u_e = f_e`
from eq(1)
`M = - \frac{v_o}{ u_o}\times\frac{D}{f_e}` ....(4)
If object AB is very close to the first focus of the objective lens, then `u_o=f_o`
If A'B' is very near to the eye lens, then `v_o = L`= the tubelength of the microscope
From eq(3)
`M = - \frac{L}{ f_o} (1 + \frac{D}{f_e})`
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