physics-class-12-unit-09-chapter-06-power-ofa-lens-and-combination-of-thin-lensesin-contact-l-6-9-qprh59srh5e

### <Success style="font-size:25px"> Power Ofa Lens And Combination Of Thin Lensesin Contact L-6 </Success>
### <primary style="font-size:24px"> Thin Lens Formula </primary>
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- Refraction Formation by a Lens

- $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$, with

- $\frac{1}{f} = (\frac{n_2}{n_1} - 1)(\frac{1}{R_1} - \frac{1}{R_2})$

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

- Converging Lens

- **Image Formation**

- Diverging Lens

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<footer style = "font-size: 18px"> $\rightarrow$ Power of a Lens and Combination of thin Lenses in Contact $\rightarrow$ <span style = "color:blue"> Thin Lens Formula </span> $\rightarrow$ Solution $\rightarrow$ Solution </footer>

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### <primary style="font-size:24px"> Solution </primary>
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- A $2 \{cm}$ long needle is placed erect at a distance of $10 \{cm}$ in front of a thin biconcave lens of focal length $10 \{cm}$.

- 1. Determine the position and the size of the image
- 2. Draw a ray diagram (with appropriate numbers for the object distance, image distance, ste.) showing formation of the image.

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-12-unit-09-chapter-06-power-ofa-lens-and-combination-of-thin-lensesin-contact-l-6_9-qprh59srh5e-060-0271.2.jpg)

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<footer style = "font-size: 18px">Power of a Lens and Combination of thin Lenses in Contact $\rightarrow$ Thin Lens Formula $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Solution $\rightarrow$ Exercise-2 </footer>

### <Success style="font-size:25px"> Power Ofa Lens And Combination Of Thin Lensesin Contact L-6 </Success>
### <primary style="font-size:24px"> Solution </primary>
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- $ u=-10 \{cm}$

- $f = -10 \{cm}$

- $\frac{1}{v}=\frac{1}{f}+\frac{1}{u} $

- $ =-\frac{1}{10}-\frac{1}{10}=-\frac{2}{10}=-\frac{1}{5} $

- $ v=-5 \{cm} $

- $ m=\frac{v}{u}=\frac{-5 \{cm}}{-10 \{cm}}=0.5 $

- size of the image = $0.5 \times 2 \{cm} $

- $ =1 \{cm}$

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<footer style = "font-size: 18px">Thin Lens Formula $\rightarrow$ Solution $\rightarrow$ <span style = "color:blue"> Solution </span> $\rightarrow$ Exercise-2 $\rightarrow$ Exercise-2 </footer>

### <Success style="font-size:25px"> Power Ofa Lens And Combination Of Thin Lensesin Contact L-6 </Success>
### <primary style="font-size:24px"> Exercise-2 </primary>
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- A particular lens, made of glass of refractive index 1.5, has a focal length ' $f$ in air $(n=1)$. When the lens is immersed in a liquid, the focal length increases to $4 f$. Determine the refractive index of the liquid.

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<footer style = "font-size: 18px">Solution $\rightarrow$ Solution $\rightarrow$ <span style = "color:blue"> Exercise-2 </span> $\rightarrow$ Exercise-2 $\rightarrow$ Power of a Lens </footer>

### <Success style="font-size:25px"> Power Ofa Lens And Combination Of Thin Lensesin Contact L-6 </Success>
### <primary style="font-size:24px"> Exercise-2 </primary>
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- $\begin{aligned} & \frac{1}{4 f}=\left(\frac{1}{\{n}_l}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)-(2) \\\ & 4=\left(\frac{n_g-n_a}{n_a}\right) \frac{n_l}{\left(n_g-n_l\right)}=\left(\frac{1.5-1}{1}\right)\left(\frac{n_l}{n_g-n_l}\right) \\\ & 8=\frac{ n_l}{\left(1.5-n_l\right)} \\\ & 8\left(1.5-n_l\right)=n_l \\\ & \quad 9 n_l=12 \\\ & n_l=\frac{12}{9}=\frac{4}{3}=1.33\end{aligned}$

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<footer style = "font-size: 18px">Solution $\rightarrow$ Exercise-2 $\rightarrow$ <span style = "color:blue"> Exercise-2 </span> $\rightarrow$ Power of a Lens $\rightarrow$ Power of a Lens </footer>

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### <primary style="font-size:24px"> Power of a Lens </primary>
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- The "converging" (or "diverging") capability of a lens is quantified by the parameter "Power of a lens", $P$

- Intuitively, the converging capability $\propto \frac{1}{f}$

- $\therefore Power \propto \frac{1}{f}$

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<footer style = "font-size: 18px">Exercise-2 $\rightarrow$ Exercise-2 $\rightarrow$ <span style = "color:blue"> Power of a Lens </span> $\rightarrow$ Power of a Lens $\rightarrow$ Power of a Lens </footer>

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### <primary style="font-size:24px"> Power of a Lens </primary>
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- Defined as $P=\frac{1}{f},  f$ in meter

- Unit is $m^{-1}$, also called 'Dioptre' (D)

- Thus, for example, a convex lens of focal length $50 \mathrm{~cm}$ has power -

- $P=\frac{1}{0.5 m}=2 D$

- Similarly a concave lens of focal length $40 \{cm}$ has power -

- $P=\frac{1}{-0.4 \{m}}=-2.5 \{D}$

- In common terms, the unit 'D' is dropped, and people tend to use +2,-2.5, etc.

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<footer style = "font-size: 18px">Power of a Lens $\rightarrow$ Power of a Lens $\rightarrow$ <span style = "color:blue"> Power of a Lens </span> $\rightarrow$ Concave Lens $\rightarrow$ Combination of Thin Lenses in Contact </footer>

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### <primary style="font-size:24px"> Combination of Thin Lenses in Contact </primary>
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- Consider two thin lenses $L_1$ and $L_2$ of focal lengths $f_1$ and $f_2$, placed in contact:

- what would be the focal length of the combination?

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<footer style = "font-size: 18px">Power of a Lens $\rightarrow$ Concave Lens $\rightarrow$ <span style = "color:blue"> Combination of Thin Lenses in Contact </span> $\rightarrow$ Combination of Thin Lenses in Contact $\rightarrow$ Successive Application of the Thin Lens Formula </footer>

- Lens formula by "successive application"

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<footer style = "font-size: 18px">Concave Lens $\rightarrow$ Combination of Thin Lenses in Contact $\rightarrow$ <span style = "color:blue"> Combination of Thin Lenses in Contact </span> $\rightarrow$ Successive Application of the Thin Lens Formula $\rightarrow$ Combination of Thin Lenses </footer>

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### <primary style="font-size:24px"> Successive Application of the Thin Lens Formula </primary>
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- Since the lenses are "thin', we assume the optical centres to coincide midway between the two lenses, at $P$.

- **For the image formed by $\mathrm{L}_1$**

- $\frac{1}{v_1}-\frac{1}{u}=\frac{1}{f_1}$

- **For the image formed by $\mathrm{L}_2$**

- $\frac{1}{v}-\frac{1}{v_1}=\frac{1}{f_2}$

- $I_1$ is the virtual object for $L_2$

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<footer style = "font-size: 18px">Combination of Thin Lenses in Contact $\rightarrow$ Combination of Thin Lenses in Contact $\rightarrow$ <span style = "color:blue"> Successive Application of the Thin Lens Formula </span> $\rightarrow$ Combination of Thin Lenses $\rightarrow$ Combination of Several Lenses </footer>

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### <primary style="font-size:24px"> Combination of Thin Lenses </primary>
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- Adding Equations (1) and (2).

- $\frac{1}{v}-\frac{1}{u}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{f}$  (say)

- i.e. with $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$, we have $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

- $\Rightarrow$ the same form as the thin lens formula for a lens of focal length 'f'.

- Since $\frac{1}{f} = P$, power of the lens

- $P = P_1+P+2$

- $P_1 = \frac{1}{f_1}, P_2 = \frac{1}{f_2}$

- $\Rightarrow$ The combination behaves like an equivalent lens of focal length 'f'.

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<footer style = "font-size: 18px">Combination of Thin Lenses in Contact $\rightarrow$ Successive Application of the Thin Lens Formula $\rightarrow$ <span style = "color:blue"> Combination of Thin Lenses </span> $\rightarrow$ Combination of Several Lenses $\rightarrow$ Example-1 </footer>

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### <primary style="font-size:24px"> Combination of Several Lenses </primary>
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- $f_1, f_2, f_3$ and $f_4$ may have different signs, in. +va. or -va

- $\therefore P_{eq}$ is the algebraic sum of the powers of individual lenses.

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<footer style = "font-size: 18px">Successive Application of the Thin Lens Formula $\rightarrow$ Combination of Thin Lenses $\rightarrow$ <span style = "color:blue"> Combination of Several Lenses </span> $\rightarrow$ Example-1 $\rightarrow$ Example-2 </footer>

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### <primary style="font-size:24px"> Example-1 </primary>
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- What is the focal length of the combination of two thin lenses - a convex lens of focal length $30 \{cm}$, and a concave lens of focal length $20 \mathrm{~cm}$ ? Is the combination 'converging' type or diverging type?
- (Exercise from Text Book)

- Does it matter if we interchange the positions of $L_1$ and $L_2$ ?

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<footer style = "font-size: 18px">Combination of Thin Lenses $\rightarrow$ Combination of Several Lenses $\rightarrow$ <span style = "color:blue"> Example-1 </span> $\rightarrow$ Example-2 $\rightarrow$ Size of the Image </footer>

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### <primary style="font-size:24px"> Example-2 </primary>
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- Consider a linear object of height $1.2 \{cm}$ placed at a distance. of $40 \{cm}$ in front of a combination of two thin lenses in contact, as shown in the figure. Given that the focal length of the convex lens is $20 \{cm}$, and that of the concave lens is $10 \{cm}$.
- 1. Determine the position and size of the image.
- 2. Draw qualitatively the corresponding ray diagram, showing the formation of the image.

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<footer style = "font-size: 18px">Combination of Several Lenses $\rightarrow$ Example-1 $\rightarrow$ <span style = "color:blue"> Example-2 </span> $\rightarrow$ Size of the Image $\rightarrow$ Example </footer>

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### <primary style="font-size:24px"> Size of the Image </primary>
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- $ m=\frac{h'}{h}=\frac{v}{u}=\frac{-\frac{40}{3}}{-40}$ = $\frac{1}{3}$

- $ \Rightarrow \text { size of the image }=\frac{1}{3} \times 1.2 \{cm} $

- $=0.4 \{cm}$

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<footer style = "font-size: 18px">Example-1 $\rightarrow$ Example-2 $\rightarrow$ <span style = "color:blue"> Size of the Image </span> $\rightarrow$ Example $\rightarrow$ Thank You </footer>