physics-class-12-unit-09-chapter-02-the-mirror-equation-ray-optics-and-optical-instruments-l-2-9-phj8x1toia

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Ray Diagram </primary>
<hr>
<main>

- Issues:

- 1. How to determine the image of an object, placed in front of a spherical mirror?
- 2. What will be the position of the image?
- 3. Will the image be larger or smaller than the object?
- 4. Will the image be read or virtual?
- 5. Will the image be 'eract' or inverted?

</div>
<div style='float: right; width:0%;'>

![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-02-the-mirror-equation-ray-optics-and-optical-instruments-l-2_9-phj8x1toia-023-0103.2.jpg)

</div>

</main>
<hr>
<footer style = "font-size: 18px">The Mirror Equation Ray Optics and Optical Instruments $\rightarrow$ Optics $\rightarrow$ <span style = "color:blue"> Ray Diagram </span> $\rightarrow$ Ray Diagram $\rightarrow$ Ray Diagram </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Ray Diagram </primary>
<hr>
<main>

- Intersection  of any two of the 4 different rays:

- 1. Ray parallel to the principal axis.
- 2. Ray incident at the pole, P
- 3. Ray passing through the principal focus, F
- 4. Ray passing through the centre of curvature, C

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Optics $\rightarrow$ Ray Diagram $\rightarrow$ <span style = "color:blue"> Ray Diagram </span> $\rightarrow$ Ray Diagram $\rightarrow$ Reflection by a Concave Mirror </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Ray Diagram </primary>
<hr>
<main>

</div>
<div style='float: center; width:100%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Ray Diagram $\rightarrow$ Ray Diagram $\rightarrow$ <span style = "color:blue"> Ray Diagram </span> $\rightarrow$ Reflection by a Concave Mirror $\rightarrow$ Cartesian Sign Convention </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Reflection by a Concave Mirror </primary>
<hr>
<main>

- consider a linear object AB- located in front of a concave mirror

- $B P $- Object distance, $u$

- $B'P$ - Image distance, ${v}$

- CP - Radius of curvature, $R$

- $F P$ - Focal length, $f$

- $A B-$ Height (size) of abject, $h$

- $N^{\prime} B^{\prime}$ - Height (sigh) of the image, $h^{\prime}$

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Ray Diagram $\rightarrow$ Ray Diagram $\rightarrow$ <span style = "color:blue"> Reflection by a Concave Mirror </span> $\rightarrow$ Cartesian Sign Convention $\rightarrow$ Mirror Equation </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Cartesian Sign Convention </primary>
<hr>
<main>

- Distances measured w.r.t the pole (x=0, y=0)
- Coordinates of the points B,C,B and F

- Thus, BP = -u, CP = -R, FP = -f

- AB = h, A'B' = -h'

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Ray Diagram $\rightarrow$ Reflection by a Concave Mirror $\rightarrow$ <span style = "color:blue"> Cartesian Sign Convention </span> $\rightarrow$ Mirror Equation $\rightarrow$ Mirror Equation </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Mirror Equation </primary>
<hr>
<main>

- For small aperture, M is clear to the axis.

- $\Rightarrow$ D is close to P

- $\therefore$ FD $\simeq$ FP

- Also, B'F = BP - FP

- Eq(3) becomes

- $\frac{B'P-FP}{FP}$ = $\frac{B'P}{BP}$ $\rightarrow$ (4)

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Reflection by a Concave Mirror $\rightarrow$ Cartesian Sign Convention $\rightarrow$ <span style = "color:blue"> Mirror Equation </span> $\rightarrow$ Mirror Equation $\rightarrow$ Magnification </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Mirror Equation </primary>
<hr>
<main>

- Applying 'sign' convention ;

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

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

- **The mirror equation**

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

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

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

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Cartesian Sign Convention $\rightarrow$ Mirror Equation $\rightarrow$ <span style = "color:blue"> Mirror Equation </span> $\rightarrow$ Magnification $\rightarrow$ Latreal Magnification </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Magnification </primary>
<hr>
<main>

- $\triangle A' B' F$ and $\triangle F M D$ are similar.

- $\Rightarrow \frac{A' B'}{M D}=\frac{B' F}{F D}$

- or $\frac{A'B'}{A B}=\frac{B'F}{F D}$    (1)

- $\triangle$ ABP and $\triangle$ A'B'P are similiar

- $\therefore$ $\frac{A'B'}{AB} = \frac{B'P}{BP}$    (2)

- From (1) and (2),

- $\frac{B'F}{F D} = \frac{B'P}{BP}$

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Mirror Equation $\rightarrow$ Mirror Equation $\rightarrow$ <span style = "color:blue"> Magnification </span> $\rightarrow$ Latreal Magnification $\rightarrow$ Magnified Virtual Image </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Latreal Magnification </primary>
<hr>
<main>

- $m = \frac{\text{size of image}}{\text{size of object}}$ = $\frac{h'}{h}$   Also called "Linear Magnification"

- Eq(2): $\frac{A'B'}{AB} = \frac{B'P}{BP}$

- Applying sign convention,

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

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

- for the present case, v<u $\Rightarrow$ |m|<1

- m-negative  $\rightarrow$  inverted image.

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Mirror Equation $\rightarrow$ Magnification $\rightarrow$ <span style = "color:blue"> Latreal Magnification </span> $\rightarrow$ Magnified Virtual Image $\rightarrow$ Sign Convention for a Convax Mirror </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Magnified Virtual Image </primary>
<hr>
<main>

- $m = \frac{h'}{h} > 1 \Rightarrow \text{Magnified image}$

- m - positive $\Rightarrow$ Eract virtual image

- How about getting a magnified real image?

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Magnification $\rightarrow$ Latreal Magnification $\rightarrow$ <span style = "color:blue"> Magnified Virtual Image </span> $\rightarrow$ Sign Convention for a Convax Mirror $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Sign Convention for a Convax Mirror </primary>
<hr>
<main>

- BP = -u , B'P = V

- FP = f, CP = R

- AB = h, A'B' = h'

- Substituting in Eq(2).

- $\frac{A'B'}{AB} = \frac{B'P}{BP}$

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

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

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Latreal Magnification $\rightarrow$ Magnified Virtual Image $\rightarrow$ <span style = "color:blue"> Sign Convention for a Convax Mirror </span> $\rightarrow$ Example $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
<hr>
<main>

- A linear object is placed in front of a concave mirror of radius of curvature $15 \{cm}$. What will be the position and magnification of the image if the object distance is -
- 1. $10 \{cm}$,
- 2. $5 \{cm}$

- in front of the mirror.

</div>
<div style='float: right; width:0%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Magnified Virtual Image $\rightarrow$ Sign Convention for a Convax Mirror $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Example $\rightarrow$ Magnified Virtual Image </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Example </primary>
<hr>
<main>

- R = -15 cm

- f = -7.5 cm

- v = ?, m = ?

- **1. u = -10 cm**

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

- $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{7.5} - \frac{1}{-10}$

</div>
<div style='float: right; width:50%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Sign Convention for a Convax Mirror $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Example </span> $\rightarrow$ Magnified Virtual Image $\rightarrow$ Magnified Virtual Image </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Magnified Virtual Image </primary>
<hr>
<main>

- **2. u = -5 $\{cm}$**

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

- $=\frac{1}{-7.5}-\frac{1}{(-5)}=\frac{1}{5}-\frac{1}{7.5} $

- $=\frac{7.5-5}{37.5}=\frac{2.5}{37.5}=\frac{1}{15} $

- $ v=\frac{375}{25}= 15$

- $\therefore m=\frac{-v}{u}=\frac{-15}{-5}=3$

- magnified virtual image

</div>
<div style='float: right; width:0%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Example $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Magnified Virtual Image </span> $\rightarrow$ Magnified Virtual Image $\rightarrow$ Extend the Example </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Extend the Example </primary>
<hr>
<main>

- 3. u = -15 cm
- 4. u = -20 cm

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

- $\frac{1}{v} =\frac{1}{-7.5} - \frac{1}{-15} = \frac{1}{15} - \frac{1}{7.5}$

- $\frac{1}{v}  =\frac{1-2}{15}=\frac{-1}{15}=$

- $\Rightarrow v = -15 \{cm}$

</div>
<div style='float: right; width:0%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Magnified Virtual Image $\rightarrow$ Magnified Virtual Image $\rightarrow$ <span style = "color:blue"> Extend the Example </span> $\rightarrow$ Extend the Example $\rightarrow$ Mirror Equation </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Extend the Example </primary>
<hr>
<main>

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

- $\Rightarrow \frac{1}{v}=\frac{1}{-7.5}-\frac{1}{-20} =\frac{1}{20}-\frac{1}{7.5} $

- $ =\frac{7.5-20}{150}$

- $\frac{-12.5}{150}$

- $v = - \frac{150}{12.5} = -12 cm$

- $m = \frac{(-12)}{(-20)} = -0.6$

</div>
<div style='float: right; width:0%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Magnified Virtual Image $\rightarrow$ Extend the Example $\rightarrow$ <span style = "color:blue"> Extend the Example </span> $\rightarrow$ Mirror Equation $\rightarrow$ Summary </footer>

### <Success style="font-size:25px"> The Mirror Equation Ray Optics And Optical Instruments L-2 </Success>
### <primary style="font-size:24px"> Mirror Equation </primary>
<hr>
<main>

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

- was obtained by substituting the coordinates corresponding to the positions of the object, image and the principal focus.

- Therefore, in using the 'mirror equation' to determine the unknown parameter ( $u$ or $v$ or $f$ the coordinates corresponding to the known parameters must be substituted.

</div>
<div style='float: right; width:0%;'>

</div>

</main>
<hr>
<footer style = "font-size: 18px">Extend the Example $\rightarrow$ Extend the Example $\rightarrow$ <span style = "color:blue"> Mirror Equation </span> $\rightarrow$ Summary $\rightarrow$ Thank You </footer>