Name: Total Internal Reflection From Prism
Uploaded: 2019-07-19
Duration: 1 min 56 s
Description: You must have seen reflectors on a bicycle. Why are they attached to the mudguards? What use do they have? Let’s watch this video on reflectors to find out.

Question

With a neat labelled diagram explain the formation of image in a simple microscope.

Accepted Answer

A simple magnifier or microscope is a converging lens of small focal length. If the object is at a distance slightly less than the focal length of the lens, the image is virtual and closer than infinity. The near point of the normal eye is $25 cm$ . i.e. it causes some strain on the eye. Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye.

The linear magnification $m$ for the image formed at the near point $D$ by a simple microscope can be obtained by using the relation

$m = \frac{v}{u} = v (\frac{1}{v} - \frac{1}{f}) = (1 - \frac{v}{f})$

Now according to our sign convention, $v$ is negative, and is equal in magnitude to $D$ Thus, the magnification is

$m = (1 + \frac{D}{f})$

We will now find the magnification when the image is at infinity. In this case we will have to obtain the angular magnification. Suppose the object has a height $h$ . The maximum angle it can subtend, and be clearly visible (without a lens), is when it is at the near point, i.e. at a distance $D$ . The angle subtended is then given by $\tan θ_{o} = (\frac{h}{D}) \approx θ_{o}$

The angle subtended at the eye by the image when the object is at $u$ . From the relations $\frac{h^{'}}{h} = m = \frac{v}{u}$

We have the angle subtended by the image, $\tan θ_{i} = \frac{h^{'}}{- v} = (\frac{h}{- v}) \frac{v}{u} = \frac{h}{- u} \approx θ_{i}$

$\Rightarrow θ_{i} = (\frac{h}{f})$ (when $u = - f$ )

Therefore, angular magnification is $m = (\frac{θ_{i}}{θ_{o}}) = \frac{D}{f}$ .

With a neat labelled diagram explain the formation of image in a simple microscope.

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