physics-class-12-unit-09-chapter-07-viewing-objects-eyes-as-an-optical-instrument-ray-optics-l-7-9-qrkwfyt5nnc

### <Success style="font-size:25px"> Viewing Objects Eyes As An Optical Instrument Ray Optics L-7 </Success>
### <primary style="font-size:24px"> Viewing Objects </primary>
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* Objects are viewed (or seen) through the Eye
* Eye is one of the finest organs which functions like an "Optical Imaging Device"
* An image of the object is formed on the Retina, which is then perceived appropriately by the Brain.
* Limitations, when the object is very far , very small 
* Needs Optical Instruments to assist!

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<footer style = "font-size: 18px"> $\rightarrow$ Viewing Objects Eyes as an Optical Instrument Ray Optics $\rightarrow$ <span style = "color:blue"> Viewing Objects </span> $\rightarrow$ Optical Instruments $\rightarrow$ Human Eye </footer>

### <Success style="font-size:25px"> Viewing Objects Eyes As An Optical Instrument Ray Optics L-7 </Success>
### <primary style="font-size:24px"> Optical Instruments </primary>
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- Microscopes and Telescopes are optical instruments that assist the Human Eye in viewing very small ("micro") and faraway ("tale") objects, respectively.

- Eye also needs 'assisting devices' to correct "defective vision" such as -

- (i) farsightedness (Hypermetropia)

- (ii) nearsightedness (Myopia)

- To understand the above, it is necessary to know the constitution and functioning of the Eye.

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<footer style = "font-size: 18px">Viewing Objects Eyes as an Optical Instrument Ray Optics $\rightarrow$ Viewing Objects $\rightarrow$ <span style = "color:blue"> Optical Instruments </span> $\rightarrow$ Human Eye $\rightarrow$ Human Eye </footer>

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- Retina is the optical receptor where the image is formed  it comprises of large number of optical. guides called "rads" and "cones"

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<footer style = "font-size: 18px">Viewing Objects $\rightarrow$ Optical Instruments $\rightarrow$ <span style = "color:blue"> Human Eye </span> $\rightarrow$ Human Eye $\rightarrow$ Accommodation </footer>

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### <primary style="font-size:24px"> Accommodation </primary>
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- The Eye F changes as required , to keep

- The image focussed on the Retina 
- of course , there is a limit

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<footer style = "font-size: 18px">Human Eye $\rightarrow$ Human Eye $\rightarrow$ <span style = "color:blue"> Accommodation </span> $\rightarrow$ Near Point and Far Point $\rightarrow$ For Normal Vision </footer>

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* $P_n$ is near point meaning D is the "least distance for clear vision"
* The eyelensian "accommodate" upto an object distance corresponding to $P_n$.
* Similarly, 'far-point' refers to the farthest distance...

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<footer style = "font-size: 18px">Human Eye $\rightarrow$ Accommodation $\rightarrow$ <span style = "color:blue"> Near Point and Far Point </span> $\rightarrow$ For Normal Vision $\rightarrow$ Farsightedness (Hypermetropia) </footer>

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- $D \approx 25 cm$

| $Y_r$    | D        |
| -------- | -------- |
|$\sim 10$ Yrs$\sim 10$cm|
|$\sim 20-25$ Yrs|$\sim 25$cm|
|$\sim 60$ Yrs|$\sim 100-500$cm|

- $P_f \rightarrow $ farpoint

- $\rightarrow$ "Eye can be focused to infinity"

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<footer style = "font-size: 18px">Accommodation $\rightarrow$ Near Point and Far Point $\rightarrow$ <span style = "color:blue"> For Normal Vision </span> $\rightarrow$ Farsightedness (Hypermetropia) $\rightarrow$ Image Formation on the Retina </footer>

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### <primary style="font-size:24px"> Farsightedness (Hypermetropia) </primary>
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- Use of conves lens to correct farsightedness

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<footer style = "font-size: 18px">Near Point and Far Point $\rightarrow$ For Normal Vision $\rightarrow$ <span style = "color:blue"> Farsightedness (Hypermetropia) </span> $\rightarrow$ Image Formation on the Retina $\rightarrow$ Object Size </footer>

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- **Normal Lens**

- f constant; use lens formula to get v
- two rays are neccessary to determine image distance and size

- **Eye lens**

- Adjustable f , fiexed v
- One ray is efficient to determine the image size

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<footer style = "font-size: 18px">For Normal Vision $\rightarrow$ Farsightedness (Hypermetropia) $\rightarrow$ <span style = "color:blue"> Image Formation on the Retina </span> $\rightarrow$ Object Size $\rightarrow$ Angular Resolution </footer>

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- Same 'object position' different object size'

* Larger objects subtend larger angles at the Eye
* Larger area occupied by the image on the retina

- $\Rightarrow$ Better resolution and clarity of the image.

- $\because$ Larger number of rods and cones would be involved in the perception of the image.

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<footer style = "font-size: 18px">Farsightedness (Hypermetropia) $\rightarrow$ Image Formation on the Retina $\rightarrow$ <span style = "color:blue"> Object Size </span> $\rightarrow$ Angular Resolution $\rightarrow$ Angular Resolution </footer>

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* The same object at different distances will subtand different angles at the eye.
* Angle subtanded will determine the size of the image on the retina, and hence size of the object-as perceived by the brain.
* Angular resolution of the eye $\sim$ 1 are minute.

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<footer style = "font-size: 18px">Image Formation on the Retina $\rightarrow$ Object Size $\rightarrow$ <span style = "color:blue"> Angular Resolution </span> $\rightarrow$ Angular Resolution $\rightarrow$ Problem </footer>

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### <primary style="font-size:24px"> Angular Resolution </primary>
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- Q = $\frac{d}{L}$

- $Q \sim 10^{-2} rad \rightarrow$ Moon

- 1 are minute = $\frac{1}{60} \times \frac{\pi}{180} \approx 3 \times 10^{-4} rad$

- Both very small nearby objects and faraway objects subtend a small angle at the Eye.

- $\Rightarrow$ Angular resolution of the image will he poor.

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<footer style = "font-size: 18px">Object Size $\rightarrow$ Angular Resolution $\rightarrow$ <span style = "color:blue"> Angular Resolution </span> $\rightarrow$ Problem $\rightarrow$ Solution </footer>

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- The search for solution (of the above question) led to the development of "microscopes" and "telescopes".

- Q = $\frac{1 \times 10^{-6} m} {0.25 m}$

- = $4 \times 10^{-6} rad <$

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<footer style = "font-size: 18px">Angular Resolution $\rightarrow$ Problem $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Simple Microscope $\rightarrow$ Angular Magnification </footer>

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- **Use of Convex Lens as a Magnifying Glass - The Simple Microscope**

- Object at the near point:

- $\theta_0=\frac{h}{D}$

- Bringing the object closer; *Angl increases, but image. is not clear.
- Inserting the Magnifying Glass

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<footer style = "font-size: 18px">Problem $\rightarrow$ Solution $\rightarrow$ <span style = "color:blue"> Simple Microscope </span> $\rightarrow$ Angular Magnification $\rightarrow$ Angular Magnification </footer>

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- **Angular Magnification, $m_{\theta}$**

- $\theta \approx \theta' \approx \frac{h}{f}$

- $\therefore m_{\theta} = \frac{\theta}{\theta_0}$

- $m_{\theta} = \frac{D}{f}$ (Angular magnification)

- Linear Magnification m = $\frac{h'}{h} = \frac{v}{u}$

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

- Note- When the Eye is supposed to infinity, (i.e u=f)

- $\theta = \theta' = \frac{h}{f}$  (for small ($\theta$ )

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<footer style = "font-size: 18px">Solution $\rightarrow$ Simple Microscope $\rightarrow$ <span style = "color:blue"> Angular Magnification </span> $\rightarrow$ Angular Magnification $\rightarrow$ Angular Magnification </footer>