physics-class-12-unit-10-chapter-02-optics-reflection-of-light-and-formation-of-images-l-2-9-9qligkbpw60

### <Success style="font-size:25px"> Optics Reflection Of Light And Formation Of Images L-2 </Success>
### <primary style="font-size:24px"> The Laws of Reflection </primary>
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- Recall. "The Laws of Reflection"

- **(i)** $\theta_i=\theta_r$

- Angle of incidence = Angle of Reflection

- **(ii)** RP , OP and PS fix in the plane ABCD

- Raversibility of ray paths

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<footer style = "font-size: 18px"> $\rightarrow$ Optics Reflection of Light and Formation of Images $\rightarrow$ <span style = "color:blue"> The Laws of Reflection </span> $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ Reflection from Spherical Mirrors </footer>

### <Success style="font-size:25px"> Optics Reflection Of Light And Formation Of Images L-2 </Success>
### <primary style="font-size:24px"> Reflection from Spherical Mirrors </primary>
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- Circular section of a  hollow glass sphere, with a reflective coating on one surface.

- Cross sections in the $x-y$ plane

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<footer style = "font-size: 18px">Optics Reflection of Light and Formation of Images $\rightarrow$ The Laws of Reflection $\rightarrow$ <span style = "color:blue"> Reflection from Spherical Mirrors </span> $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ Reflection from Spherical Mirrors </footer>

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### <primary style="font-size:24px"> Reflection from Spherical Mirrors </primary>
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* CM is the normal at the point of incidence
* Reflection from a Concave Mirror
* Reflation from a Convex Mirror
* C. - Centre of Curvature
* $P$ - Pole

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<footer style = "font-size: 18px">The Laws of Reflection $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ <span style = "color:blue"> Reflection from Spherical Mirrors </span> $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ Reflection Parallel to the Principal Axis </footer>

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### <primary style="font-size:24px"> Reflection from Spherical Mirrors </primary>
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* ${\theta_i=\theta_r}$,${\theta_i=\theta_r}$
* Principal axis
* For $\theta_i=0, \quad \theta_r=0$
* $\Rightarrow$ The ray incident along the principal axis will be reflected back along the same path

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<footer style = "font-size: 18px">Reflection from Spherical Mirrors $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ <span style = "color:blue"> Reflection from Spherical Mirrors </span> $\rightarrow$ Reflection Parallel to the Principal Axis $\rightarrow$ Parallel Beam </footer>

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### <primary style="font-size:24px"> Reflection Parallel to the Principal Axis </primary>
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* Reflection of rays parallel to the principal axis 
* C - Centre of curvature
* F- Principal focus
* 'Converging' and 'Diverging' beams 
* cf: Parallal rays incident on a Plane Mirror

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<footer style = "font-size: 18px">Reflection from Spherical Mirrors $\rightarrow$ Reflection from Spherical Mirrors $\rightarrow$ <span style = "color:blue"> Reflection Parallel to the Principal Axis </span> $\rightarrow$ Parallel Beam $\rightarrow$ Paraxial Approximation </footer>

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### <primary style="font-size:24px"> Paraxial Approximation </primary>
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* 'para-' 'axial' $\Rightarrow$ close to the axis or nearby the axis
* Paraxial rays:
* Parallel rays, close to the axis, and oblique rays which subtend small angles with the principal axis.
* $$\theta=0-5^{\circ} \text {, say. }$$
* "Small-aperture approximation"

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<footer style = "font-size: 18px">Reflection Parallel to the Principal Axis $\rightarrow$ Parallel Beam $\rightarrow$ <span style = "color:blue"> Paraxial Approximation </span> $\rightarrow$ Paraxial Approx $\rightarrow$ Optical System </footer>

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### <primary style="font-size:24px"> Paraxial Approx </primary>
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- $\theta \rightarrow i \text { mall } $

- $0-5^{\circ}$

- $ tan \theta \approx \theta $,

- $ sin \theta \approx \theta $

- for snall  $\theta$ small aperture approximation

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<footer style = "font-size: 18px">Parallel Beam $\rightarrow$ Paraxial Approximation $\rightarrow$ <span style = "color:blue"> Paraxial Approx </span> $\rightarrow$ Optical System $\rightarrow$ Paraxial Approximation </footer>

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### <primary style="font-size:24px"> Focal Length of a Spherical Mirror </primary>
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- $tan \theta_i = \frac {MD}{CD} , tan 2\theta_i = \frac {MD}{QD} $

- For peraxial rays, point $M$ is close to $P$

- $\therefore C D \approx C P=R$, the radius of curvature llly $Q . D \approx Q . P$.

- Also, $\tan \theta_i \approx \theta_i, \tan 2 \theta_i$ $\approx 2 \theta_i$

- Gives $\theta_i=\frac{M D}{R}, 2 \theta_2=\frac{M P}{Q P} \rightarrow Q P=\frac{R}{2}$

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<footer style = "font-size: 18px">Optical System $\rightarrow$ Paraxial Approximation $\rightarrow$ <span style = "color:blue"> Focal Length of a Spherical Mirror </span> $\rightarrow$ Focal Length of a Spherical Mirror $\rightarrow$ Focal Length </footer>

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### <primary style="font-size:24px"> Focal Length </primary>
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- $Q P=\frac{R}{2}$, constant

- $M$ - is an arbitrarypoint

- $\Rightarrow$ Any parallel raywill pass through $Q$

- The point ' $Q$ ' is called the "principal focus" and' designate as ' $F$ '

- The distance FP is celled "focal length', ' $f$ '

- Thus $Q . P=F P=f$

- $\therefore f=\frac{R}{2}$

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<footer style = "font-size: 18px">Focal Length of a Spherical Mirror $\rightarrow$ Focal Length of a Spherical Mirror $\rightarrow$ <span style = "color:blue"> Focal Length </span> $\rightarrow$ Principal Axis $\rightarrow$ Formation of Images </footer>

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### <primary style="font-size:24px"> Principal Axis </primary>
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- Parallel Rays Inclined to the Principal Axis

- Parallel rays remain parallel

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<footer style = "font-size: 18px">Focal Length of a Spherical Mirror $\rightarrow$ Focal Length $\rightarrow$ <span style = "color:blue"> Principal Axis </span> $\rightarrow$ Formation of Images $\rightarrow$ Spherical Mirror </footer>

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### <primary style="font-size:24px"> Formation of Images </primary>
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- Image of a point object: Plane mirror

- $I$ is the image point

- $\triangle O A B$ and $\triangle I A B$ ara congruent. $\Rightarrow O B=I B$

- A "virtual images is formal at I.

- Point $A$ is artibrary $OB=IB$ in all cases.

- I is a "virtual image"

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<footer style = "font-size: 18px">Focal Length $\rightarrow$ Principal Axis $\rightarrow$ <span style = "color:blue"> Formation of Images </span> $\rightarrow$ Spherical Mirror $\rightarrow$ Extended Objects </footer>

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### <primary style="font-size:24px"> Spherical Mirror </primary>
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- Intersection of any two rays from the abject is sufficient to determine the image.

- The point $Q$ is arbitrary ; the object distance and image distance will satisfy a relation, independent of Q.

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<footer style = "font-size: 18px">Principal Axis $\rightarrow$ Formation of Images $\rightarrow$ <span style = "color:blue"> Spherical Mirror </span> $\rightarrow$ Extended Objects $\rightarrow$ Thank You </footer>