physics-class-12-unit-09-chapter-03-refraction-of-light-ray-optics-and-optical-instrument-l-3-9-imfjnldxf4m

### <Success style="font-size:25px"> Refraction Of Light Ray Optics And Optical Instrument L-3 </Success>
### <primary style="font-size:24px"> Reflection of Light </primary>
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- **Reflection of light from A transparent Medium**

- e = i

- r $\neq$ i

- Historically known for a long time

- Partial reflection and partial transmission of a light beam

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<footer style = "font-size: 18px"> $\rightarrow$ Refraction of Light Ray Optics and Optical Instrument $\rightarrow$ <span style = "color:blue"> Reflection of Light </span> $\rightarrow$ Air-Water Interface $\rightarrow$ Snell's Law </footer>

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### <primary style="font-size:24px"> Air-Water Interface </primary>
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- Great physicist Ptolemy tabulated in 140 AD!

- In 1621, W snell formulated

- $\frac{\sin i}{\sin r} = constant$

- based on experimental observations.

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<footer style = "font-size: 18px">Refraction of Light Ray Optics and Optical Instrument $\rightarrow$ Reflection of Light $\rightarrow$ <span style = "color:blue"> Air-Water Interface </span> $\rightarrow$ Snell's Law $\rightarrow$ Rarer to Densar </footer>

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### <primary style="font-size:24px"> Snell's Law </primary>
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- $\frac{\sin i}{\sin r} = n_2$, a constant

- $n_{2 1} \rightarrow$ refractive index of the second medium w.r.t the first

- $n_{2 1} = \frac{n_2}{n_1}$  |

- $n_{2 1} > 1$ if $n_2 > n_1$

- $n_{2 1} < 1$ if $n_2 < n_1$

- The medium with higher refractive index (of the two) is called 'densar' medium, and the medium with lower refractive index is called  the 'rarer' medium.

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<footer style = "font-size: 18px">Reflection of Light $\rightarrow$ Air-Water Interface $\rightarrow$ <span style = "color:blue"> Snell's Law </span> $\rightarrow$ Rarer to Densar $\rightarrow$ Densar to Rarer </footer>

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### <primary style="font-size:24px"> Rarer to Densar </primary>
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- $\frac{\sin i}{\sin r} = n_{2 1} > 1 $

- $\Rightarrow \sin r < \sin i$

- $\Rightarrow r < 1$

- Ray bends towards normal

- refracted ray

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<footer style = "font-size: 18px">Air-Water Interface $\rightarrow$ Snell's Law $\rightarrow$ <span style = "color:blue"> Rarer to Densar </span> $\rightarrow$ Densar to Rarer $\rightarrow$ Refraction thorugh a Glass Slab (two interfaces) </footer>

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### <primary style="font-size:24px"> Densar to Rarer </primary>
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- $\frac{\sin i}{\sin r} = n_{2 1} < 1 $

- $\Rightarrow \sin r > \sin i$

- $\Rightarrow r > 1$

- Ray bends away from normal.

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<footer style = "font-size: 18px">Snell's Law $\rightarrow$ Rarer to Densar $\rightarrow$ <span style = "color:blue"> Densar to Rarer </span> $\rightarrow$ Refraction thorugh a Glass Slab (two interfaces) $\rightarrow$ Refraction through a Multi-Layered Structure </footer>

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### <primary style="font-size:24px"> Refraction thorugh a Glass Slab (two interfaces) </primary>
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- $n_1 = n_{air} = n_3$

- $n_2 = n_{glass}$

- t- thickness of the glass

- l- lateral shift

- Applying snell's Law at interfaces (i) and (ii):

- $\frac{\sin \theta_1} {\sin \theta_2}$ = $\frac{n_{glass}}{n_{air}}$ ; $\frac{\sin \theta_2}{\sin \theta_3}$ = $\frac{n_{air}}{n_{glass}}$

- Gives $\sin \theta_1 = \sin \theta_3 = \theta_1 = \theta_3$

- No derivation, but lateral shift of ray.

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<footer style = "font-size: 18px">Rarer to Densar $\rightarrow$ Densar to Rarer $\rightarrow$ <span style = "color:blue"> Refraction thorugh a Glass Slab (two interfaces) </span> $\rightarrow$ Refraction through a Multi-Layered Structure $\rightarrow$ Laws of Refraction </footer>

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### <primary style="font-size:24px"> Refraction through a Multi-Layered Structure </primary>
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- $ \frac{\sin \theta_1}{\sin \theta_2}=\frac{n_2}{n_1} $

- $ n_1 \sin \theta_1=n_2 \sin \theta_2 $

- $ n_2 \sin \theta_2=n_3 \sin \theta_3 $

- $ n_3 \sin \theta_3=n_4 \sin \theta_4 $

- $ n_5 \sin \theta_5=n_6 \sin \theta_6 $

- $ \Rightarrow n_1 \sin \theta_1=n_6 \sin \theta_6 $

- If the first and the last medium are the same (Air in this case), then $\theta_1 = \theta_6 \Rightarrow$ No derivation!

- i.e The final emergence angle ($\theta_6$) does not depend on the thickness and ref index of layers!

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<footer style = "font-size: 18px">Densar to Rarer $\rightarrow$ Refraction thorugh a Glass Slab (two interfaces) $\rightarrow$ <span style = "color:blue"> Refraction through a Multi-Layered Structure </span> $\rightarrow$ Laws of Refraction $\rightarrow$ Some Natural Consequences of Refraction </footer>

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### <primary style="font-size:24px"> Laws of Refraction </primary>
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- 1. The incident ray, the reflected ray and the transmitted ray (or refracted ray) lie in a plane, perpendicular the interface.
- 2. $\frac{\sin \theta_i}{\sin theta_r}$ = $n_{2 1}$ = $\frac{n_2}{n_1}$ (Snell's Law).

- or $n_1 \sin \theta_1$ = $n_2 \sin \theta_2$

- $\theta_1$ or $\theta_2$ could be the angle of incidence.

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<footer style = "font-size: 18px">Refraction thorugh a Glass Slab (two interfaces) $\rightarrow$ Refraction through a Multi-Layered Structure $\rightarrow$ <span style = "color:blue"> Laws of Refraction </span> $\rightarrow$ Some Natural Consequences of Refraction $\rightarrow$ Apparent Depth </footer>

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### <primary style="font-size:24px"> Some Natural Consequences of Refraction </primary>
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- A. 'Apparent Depth'

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<footer style = "font-size: 18px">Refraction through a Multi-Layered Structure $\rightarrow$ Laws of Refraction $\rightarrow$ <span style = "color:blue"> Some Natural Consequences of Refraction </span> $\rightarrow$ Apparent Depth $\rightarrow$ Inclination of the Setting Sun </footer>

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### <primary style="font-size:24px"> Apparent Depth </primary>
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- d- Actual depth

- d'- Apparent depth

- For small angles i and r,

- $\sin i \simeq \tan i \simeq \frac{QR}{PQ}$

- $\sin r \simeq \tan r \simeq \frac{QR}{P'Q}$

- $\therefore \frac{n_2}{n_1}$ = $\frac{\sin i}{\sin r}$ = $\frac{P'Q}{PQ}$ = $\frac{d'}{d}$

- i.e $\frac{Apparent Depth}{Actual Depth}$ = $\frac{n_2}{n_1}$

- Usually, $n_2 = 1$ - as in our example

- $\therefore \text{Apparent Depth} = \frac{Actual Depth}{Ref. index of medium}$

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<footer style = "font-size: 18px">Laws of Refraction $\rightarrow$ Some Natural Consequences of Refraction $\rightarrow$ <span style = "color:blue"> Apparent Depth </span> $\rightarrow$ Inclination of the Setting Sun $\rightarrow$ Inclination of the Setting Sun </footer>

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### <primary style="font-size:24px"> Inclination of the Setting Sun </primary>
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- S' - Apparent position of the sun

- O - Observer

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<footer style = "font-size: 18px">Some Natural Consequences of Refraction $\rightarrow$ Apparent Depth $\rightarrow$ <span style = "color:blue"> Inclination of the Setting Sun </span> $\rightarrow$ Inclination of the Setting Sun $\rightarrow$ Example-1 </footer>

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### <primary style="font-size:24px"> Example-1 </primary>
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- A narrow beam of light travels from Medium 1 through three layers of different transparent media into Medium 5, as shown in the figure. Rank the media in ascending order of their refractive indices.

- Use snell's law: $n_1 . \sin r = constant$

- (i) Medium 4
- (ii) Medium 1
- (iii) Medium 3
- (iv) Medium 5
- (v) Medium 2

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<footer style = "font-size: 18px">Inclination of the Setting Sun $\rightarrow$ Inclination of the Setting Sun $\rightarrow$ <span style = "color:blue"> Example-1 </span> $\rightarrow$ Problem $\rightarrow$ Example </footer>

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### <primary style="font-size:24px"> Problem </primary>
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- A glass beaker of height $10 \{cm}$ contains water $(n=1.33)$ up to $4 \{cm}$ height from the bottom, and then a transparent oil $(n=1.31)$ above water, upto the top edge of the beaker. When viewed from above, what would be the apparent depth of a small coin located at the bottom of the beaker?

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<footer style = "font-size: 18px">Inclination of the Setting Sun $\rightarrow$ Example-1 $\rightarrow$ <span style = "color:blue"> Problem </span> $\rightarrow$ Example $\rightarrow$ Solution </footer>

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### <primary style="font-size:24px"> Solution </primary>
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- $ \frac{x_3}{h}=\tan \theta_3 $

- $ h=\frac{x_3}{\tan \theta_3}$ = $\frac{x_1+x_2}{\tan \theta_3} $

- $ x_1=h_1 \tan \theta_1, x_2=h_2 \tan \theta_2 $

- $\therefore  h=h_1 \frac{\tan \theta_1}{\tan \theta_3}+h_2 \frac{\tan \theta_2}{\tan \theta_3}$  (eqn-1)_

- For any $\theta_3, \theta_1$ and $\theta_2$ can be determined using snell's law.

- "Viewing from above"

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

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### <primary style="font-size:24px"> Solution </primary>
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- $\Rightarrow \theta_3, \theta_2, \theta_1$ are small

- $\therefore \tan \theta_3 \simeq \sin \theta_3, \tan \theta_2 \simeq \sin \theta_2$ and $\tan \theta_1 \simeq \sin \theta_1$.

- h- Apparent depth of p

- $x_3 = x_1 + x_2$

- $h = \frac{h_1}{n_2} + \frac{h_2}{n_2}$  (eqn-2)

- with $n_3 = 1$(air)

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

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### <primary style="font-size:24px"> Solution </primary>
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- $\frac{h_1}{n_1}+\frac{h_2}{n_2}$

- $l'=\frac{t}{n}+\frac{(l-b)}{1}$

- $l-l'=t (1-\frac{1}{n})$

- $s=t(1-\frac{1}{n})$

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<footer style = "font-size: 18px">Solution $\rightarrow$ Solution $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Find the Expression for I $\rightarrow$ Thank You </footer>