What is a simple microscope ? With the help of a diagram, explain the working of a simple microscope. Also write the uses of simple microscope.
A simple microscope is a converging lens of small focal length to see very small objects as magnified one.
It consists of a convex lens of small focal length. A magnifying glass is an example of a simple microscope.
Principle : A simple microscope is based upon the fact that an object placed between the optical centre and the focus of a convex lens, forms a virtual, erect and magnified image on the same side of the lens.
The image is formed at the least distance of distinct vision (i.e. 25 cm) from the eye.
Working : Consider a convex lens of focal length $f$. Let AB be an object which lies between the optical centre (C) and the focus (F) of the lens. The rays of light from the object do not meet after refraction through the lens. They appear to come from a point B' so that A'B' is the virtual image of the object AB. This image is erect and magnified (i.e. large in size). Thus, magnified image (say A'B') of object (say AB) will be viewed by the eye
Uses of Simple microscope :
(i) It is used by jewellers and watch makers for precision work.
(ii) It is used by students in the laboratory for reading the Vernier scales of vernier callipers, travelling microscopes, spectrometers and other instruments.
MAGNIFYING POWER (OR ANGULAR MAGNIFICATION) :
Find the expression for its magnifying power when the image is formed at least distance of distinct vision
Case 1 : For distinct vision when the image is formed at least distance of distinct vision.
STEP 1. Let to be the angle subtended by the object at the eye when the object is supposed to be kept at the least distance of distinct vision and $\beta$ be the angle subtended by the image at the eye, when image is at the distance equal to the least distance of distinct vision.
Magnifying power, $M.P. = \frac{\beta}{\alpha}$
STEP 2. Applying Sign Conventions :
$\alpha$ and $\beta$ are small angles, so using the relation $\theta = l/r$, we get
$\beta = \frac{A'B'}{CA'}$
and
$\alpha = \frac{A'P}{CA'}$
$M.P. = \frac{A'B'/CA'}{A'P/CA'} = \frac{A'B'}{AB} \quad (\because A'P = AB)$
or
$M.P. = \frac{\text{Size of image }(h')}{\text{Size of object }(h)}$
But for a convex lens,
$m = \frac{h'}{h} = -\frac{v}{u}$
Since, $v = -D$ and $u = -u$, we get $M.P. = -\frac{-D}{-u} = \frac{D}{u}$
Hence eqn. (i) becomes,
$M.P. = \frac{D}{u} \quad \cdots (iii)$
$M.P. = \frac{D}{u}$
STEP 3. Using lens formula
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \quad \cdots (iv)$
Applying new Cartesian sign conventions : $u$ becomes $-u$ and $v = -D$, we get
$$-\frac{1}{D} - \frac{1}{-u} = \frac{1}{f}$$
$\frac{1}{u} - \frac{1}{D} = \frac{1}{f}$$
Multiplying by $D$, we get,
$$\frac{D}{u} - 1 = \frac{D}{f}$
$\frac{D}{u} = 1 + \frac{D}{f}$
Substituting the value of eqn. (v) in eqn. (iii), we get
$M.P. = 1 + \frac{D}{f} \quad \cdots (vi)$
When image formed by simple microscope is at the least distance of distinct vision magnifying power is given by
$M.P. = 1 + \frac{D}{f} \quad \text{or} \quad M.P. = \frac{D}{u}$
Drive An expression for the magnifying Power of a Simple microscope when the image is formed at infinity.
Case 2 : For Normal Vision (When the image is formed at infinity) :
Drive an expression for the magnifying power of a simple microscope when the image is formed at infinity.
To see the image with relaxed eye, the image must be formed at infinity [Figure 94]. The microscope is in normal adjustment when the image is formed at infinity, i.e. $v = \infty$.
For perfectly relaxed normal eye, the far point is at infinity so that object must be placed at the focus of the lens.
For a lens,
$\frac{1}{u} - \frac{1}{v} = \frac{1}{f}$
Here,
$u = -u \quad \text{and} \quad v = -\infty$
$\therefore \quad \frac{1}{u} = \frac{1}{f}$
Multiplying both sides by $D$, we get
$\frac{D}{u} = \frac{D}{f}$
Magnifying power,
$M.P. = \frac{\beta}{\alpha} = \frac{BD}{BA} = \frac{D}{u}$
But
$u = f$
$\therefore \quad M.P. = \frac{D}{f}$