Light - Reflection and Refraction

 Light - Reflection and Refraction 

1. Introduction to Light

• Definition: Light is a form of energy that enables us to see objects. It travels in straight lines (rectilinear propagation).
• Nature: Light is an electromagnetic wave that does not require a medium to propagate.
• Speed: In a vacuum, the speed of light is approximately 3x10⁸ m/s

2. Reflection of Light

• Definition: Reflection is the phenomenon where light bounces back into the same medium after striking a polished or shiny surface (e.g., a mirror).
• Types of Reflection:
• Regular Reflection: Occurs on smooth surfaces (e.g., plane mirrors), producing a clear image.
• Diffuse Reflection: Occurs on rough surfaces (e.g., paper), scattering light in multiple directions, no clear image formed.
• Laws of Reflection:

1.              The angle of incidence (angle i) is equal to the angle of reflection (angle r).

2.              The incident ray, the reflected ray, and the normal at the point of incidence lie in the same plane.

• Key Terms:

• Incident Ray: The ray of light that strikes the surface.
• Reflected Ray: The ray that bounces back after reflection.
• Normal: A perpendicular line drawn at the point of incidence.
• Angle of Incidence: The angle between the incident ray and the normal.
• Angle of Reflection: The angle between the reflected ray and the normal.

Plane Mirror

• Characteristics of Image Formed by a Plane Mirror:
1. Virtual (cannot be obtained on a screen).
2. Erect (upright).
3. Same size as the object.
4. Laterally inverted (left-right reversal).
5. Formed at the same distance behind the mirror as the object is in front of it.
• Uses of Plane Mirrors:

• In dressing tables, bathrooms, and salons.
• In periscopes and kaleidoscopes.

Spherical Mirrors

• Definition: Mirrors with a curved reflecting surface, part of a sphere.
• Types:
• Concave Mirror: Reflecting surface is curved inward (e.g., shaving mirror).
• Convex Mirror: Reflecting surface is curved outward (e.g., side mirrors in vehicles).
• Key Terms:
• Pole (P): The center of the reflecting surface.
• Center of Curvature (C): The center of the sphere of which the mirror is a part.
• Radius of Curvature (R): The radius of the sphere ((R = 2f)).
• Principal Axis: The straight line passing through the pole and the center of curvature.
• Focus (F): The point where parallel rays converge (concave) or appear to diverge from (convex) after reflection.
• Focal Length (f): The distance between the pole and the focus ((f = R/2)).
• Rules for Ray Diagrams (for image formation):

1.              A ray parallel to the principal axis passes through the focus (concave) or appears to diverge from the focus (convex) after reflection. NCERT Fig 10.3

2.              A ray passing through the focus (concave) or directed toward the focus (convex) becomes parallel to the principal axis after reflection. NCERT Fig 10.4

3.              A ray passing through the center of curvature (concave) or directed toward it (convex) retraces its path after reflection. NCERT Fig 10.5

4.              A ray incident at the pole is reflected with the same angle relative to the principal axis. NCERT Fig 10.6

• Image Formation by Concave Mirror:

Position of Object	Position of Image	Nature of Image	Size of Image	Example Use
At infinity	At focus (F)	Real, inverted	Highly diminished	Searchlights
Beyond C	Between F and C	Real, inverted	Diminished	Projectors
At C	At C	Real, inverted	Same size	Shaving mirror
Between C and F	Beyond C	Real, inverted	Enlarged	Makeup mirror
At F	At infinity	Real, inverted	Highly enlarged	Telescopes
Between F and P	Behind mirror	Virtual, erect	Enlarged	Dentist’s mirror

                              

Uses of Concave Mirrors

- Used in torches, search lights and headlights of vehicles, to get powerful parallel beams of light.

- Used in shaving mirrors to see larger image of the face.

- used by dentists to see larger images of the teeth of patients.

- Used to converge sunrays on a point to produce large amount of concentrated heat in a solar furnace

• Image Formation by Convex Mirror:

• Image is always virtual, erect, and diminished, formed between the pole and focus, regardless of the object’s position.
• Uses: Rearview mirrors, streetlight reflectors.

                       

                                            Diagrams 

• Uses of Convex Mirror
• It is used as rear view mirrors in vehicles because they always give an erect image and have wider field of view as they are curved outward.
• Used as shop security mirrors.
• Sign Convention (New Cartesian Sign Convention):
• All distances are measured from the pole.
• Distances to the left of the pole (incident light direction) are negative.
• Distances to the right of the pole are positive.
• Heights above the principal axis are positive; below are negative.

Mirror Formula:

Magnification:

The ratio of the size of the image to that of the object is called magnification. For a mirror, magnification (m) is given by.

 m=hi/ho

Also , m = -v/u,

Therefore , m = -v/u=hi/ho

If m>1, then hi>ho

If m=1, then hi=ho

If m<1, then hi<ho

1. Refraction of Light:

Refraction is the bending of light when it passes from one transparent medium to another. This bending occurs due to the change in speed of light in different media.

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2. Cause of Refraction:

The main cause of refraction is the change in the speed of light as it moves from one medium to another:

• When light moves from rarer to denser medium, it slows down and bends towards the normal.

• When light moves from denser to rarer medium, it speeds up and bends away from the normal.

🔸 Rarer medium: A medium in which light travels faster (e.g., air).
🔸 Denser medium: A medium in which light travels slower (e.g., glass, water).

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3. Examples of Refraction of Light:

1. A pencil appears bent when partly immersed in water.

2. A coin placed in water appears raised.

3. The apparent depth of a swimming pool is less than its real depth.

4. Light entering the eye through a spectacle lens.

5. Formation of a rainbow (due to refraction and reflection in raindrops).

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4. Refraction of Light Through a Rectangular Glass Slab:

When a ray of light passes through a rectangular glass slab, the emergent ray is parallel to the incident ray, but displaced laterally (sideways).

Important Points:

• Incident Ray (AB): The ray entering the glass slab.

• Refracted Ray (BC): The ray that bends inside the glass.

• Emergent Ray (CD): The ray that emerges out of the slab.

• Angle of Incidence (∠i): Angle between incident ray and normal.

• Angle of Refraction (∠r): Angle between refracted ray and normal.

• Angle of Emergence (∠e): Angle between emergent ray and normal (∠i = ∠e).

• Lateral Displacement: The perpendicular distance between the path of the incident ray and emergent ray.

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🔹 5. Laws of Refraction of Light:

1. First Law: The incident ray, the refracted ray, and the normal all lie in the same plane.

2. Second Law (Snell's Law):
   The ratio of sine of the angle of incidence to the sine of the angle of refraction is a constant:

   $$\mu$$

   Where,

   • $\mathrm{<br>}$ = angle of incidence

   • $r$= angle of refraction

   • $\mathrm{<br>}$ = refractive index

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6. Refractive Index (μ):

Refractive Index is a measure of extent of the change in direction of ray of light that takes place in a given pair of media.

🔸 Absolute Refractive Index:

When light travels from vacuum (or air) to a medium:

$$\mu =\; c/v$$

Where,

• $\mathrm{<span\; style="font-family:\; "Times\; New\; Roman",\; serif;">\mu =\; refractive\; index\; of\; the\; medium</span>}$

• $c$= speed of light in vacuum ( $3\times {\mathrm{10^}}^{8}m\mathrm{/}\mathrm{s)}$

• $v$= speed of light in the medium

• ${\mathrm{<span\; style="font-family:\; "Times\; New\; Roman",\; serif;"> </span>}}_{}$

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🔹 7. Relation Between Refractive Index and Speed of Light:

$$\mu =\frac{\mathrm{<span\; face="RedditSans,\; "sans-serif""\; style="font-weight:\; bolder;"> \; c\; /\; v</span><span\; face="RedditSans,\; "sans-serif""\; style="font-weight:\; bolder;"><br></span><span\; face="RedditSans,\; "sans-serif""\; style="font-weight:\; bolder;"><br></span><span><span\; style="background-color:\; transparent;\; font-family:\; "Times\; New\; Roman",\; serif;\; font-weight:\; bolder;"></span></span>}}{}$$

$$\frac{\mathrm{<span\; face="RedditSans,\; sans-serif"\; style="font-weight:\; bolder;"><span\; style="background-color:\; transparent;\; font-family:\; "Times\; New\; Roman",\; serif;\; font-weight:\; bolder;">Lens</span></span>}}{}$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;">Lens\; is\; a\; transparent\; medium\; bounded\; by\; two\; surfaces\; of\; which\; one\; or\; both\; surfaces\; are\; spherical.</span>}}{}$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;">Types</span>}}{}$$

$$1. Convex or Converging Lens- A lens which is thicker at the centre and thinner at its ends is called convex lens. It is also called as converging lens because it converges the light rays passing through it. A double convex lens is called convex lens.2. Concave or Diverging Lens - A lens which is thinner at the centre and thicker at its ends is called a concave lens. It is also known as diverging lens because it diverges a parallel beam of light passing through it. A doubly concave lens is simply called concave lens.Image formation in lenses using ray diagrams$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;">1.\; If\; ray\; of\; light\; is\; parallel\; to\; principal\; axis\; ,\; it\; gets\; refracted\; through\; focus.</span>}}{}$$

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$$\frac{\mathrm{<div\; class="separator"\; style="clear:\; both;\; text-align:\; center;"><a\; href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGyvi3rG0MsWFHr5jNxm\_WB1wgmOKhV8Y6yQ0x8dC9Y2-78iPSVDyacSwFrH7A\_EaAdFIrN5GDG1t1AcST7RkuHUrvj1KF\_s8-LAIkuBEvWy2yMNwtyP-97uBADt\_-WkzJD-S\_MmNvzS2igQfF7iT46nG9hSdNmxNw0p8C2J6awxURzpiKtrWMQUZHOyc/s749/Pic\%201.jpeg"\; imageanchor="1"\; style="margin-left:\; 1em;\; margin-right:\; 1em;"><img\; border="0"\; data-original-height="231"\; data-original-width="749"\; height="198"\; src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGyvi3rG0MsWFHr5jNxm\_WB1wgmOKhV8Y6yQ0x8dC9Y2-78iPSVDyacSwFrH7A\_EaAdFIrN5GDG1t1AcST7RkuHUrvj1KF\_s8-LAIkuBEvWy2yMNwtyP-97uBADt\_-WkzJD-S\_MmNvzS2igQfF7iT46nG9hSdNmxNw0p8C2J6awxURzpiKtrWMQUZHOyc/w640-h198/Pic\%201.jpeg"\; width="640"></a></div><br><span\; style="font-family:\; Times\; New\; Roman,\; serif;"><br></span>}}{}$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;">2.\; If\; ray\; of\; light\; passes\; through\; the\; focus,\; it\; gets\; refracted\; and\; goes\; parallel\; to\; principal\; axis.</span>}}{}$$

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$$\frac{\mathrm{<div\; class="separator"\; style="clear:\; both;\; text-align:\; center;"><a\; href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgih3boK0Nfcwn9I-aoNwV7x4CLPDXqi0Zg8qNzmcRZAE5dtwOgl0PXpjDLOekTOXJWVGcpgCnwW9HcTPlBt6Hkvoh6Tk-7du9Jis\_-gPz6D7YOabwemsnV3iXuPvYRe69XTczq3V\_-GY\_rZtDlu9vb8yHvKamzPzzNCEPl9QRTYge1ynvVPDLVzYADb0M/s688/Pic\%202.jpeg"\; imageanchor="1"\; style="margin-left:\; 1em;\; margin-right:\; 1em;"><img\; border="0"\; data-original-height="287"\; data-original-width="688"\; height="266"\; src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgih3boK0Nfcwn9I-aoNwV7x4CLPDXqi0Zg8qNzmcRZAE5dtwOgl0PXpjDLOekTOXJWVGcpgCnwW9HcTPlBt6Hkvoh6Tk-7du9Jis\_-gPz6D7YOabwemsnV3iXuPvYRe69XTczq3V\_-GY\_rZtDlu9vb8yHvKamzPzzNCEPl9QRTYge1ynvVPDLVzYADb0M/w640-h266/Pic\%202.jpeg"\; width="640"></a></div><br><span\; style="font-family:\; Times\; New\; Roman,\; serif;"><br></span>}}{}$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;"><br></span>}}{}$$

$$\frac{\mathrm{<span\; style="font-family:\; Times\; New\; Roman,\; serif;">3.\; If\; ray\; of\; light\; passes\; through\; optical\; centre,\; then\; passes\; it\; without\; any\; deviation.</span>}}{}$$

$$\frac{\mathrm{<div\; class="separator"\; style="clear:\; both;\; text-align:\; center;"><a\; href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijOLXO3woiouEP-Y9Qjw8Lz9VV-\_ccPGouu01I6Dij4iDDGaEQ44ACIX9mPLmEk8gl7xDJN508V3FRa89O-8pxCPl46-KZEpNjFykGNA1IkGZxLNdy3oTtRlmhaLKYe0uI7CIV\_4jdVJioROOEAnj5E\_WhB0z8OOUw5PJb8H1CQvY6-ZR\_e\_rJlvSGi4c/s672/Pic\%203.jpeg"\; imageanchor="1"\; style="margin-left:\; 1em;\; margin-right:\; 1em;"><img\; border="0"\; data-original-height="197"\; data-original-width="672"\; height="188"\; src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijOLXO3woiouEP-Y9Qjw8Lz9VV-\_ccPGouu01I6Dij4iDDGaEQ44ACIX9mPLmEk8gl7xDJN508V3FRa89O-8pxCPl46-KZEpNjFykGNA1IkGZxLNdy3oTtRlmhaLKYe0uI7CIV\_4jdVJioROOEAnj5E\_WhB0z8OOUw5PJb8H1CQvY6-ZR\_e\_rJlvSGi4c/w640-h188/Pic\%203.jpeg"\; width="640"></a></div><br><span\; style="font-family:\; Times\; New\; Roman,\; serif;">Image\; formation\; by\; convex\; lens:</span>}}{}$$

$$a) Object at : Infinity, Image at : F1, Nature and size: Real and inverted, Highly diminished or point size$$

b) Object : Beyond of centre of curvature

        Image : Between F2 and 2F2

Nature and size: real and inverted, diminished

c) Object at : 2F1

     Image at : 2F2

    Nature and size: real and inverted, diminished.

d) Object at : between 2F1 and F1

     Image at : beyond 2F2

    Nature and size: Real and inverted, magnified

e) Object at : At F1

     image at : at  infinity

nature : real and inverted

f) Object between F1 and O

   Image : beyond 2 F1

nature and size: virtual erect , magnified

    

Image formation by concave mirror

$$\frac{\mathrm{<div\; class="separator"\; style="clear:\; both;\; text-align:\; center;"><a\; href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgosZLEVSjiEvXwflDd5koI\_hSFfhJEHop0lANj1kdHLA2EjNPAmIj\_ioCd0Vx7qMDl9buOxYZCJtAM1qIe5Ma7QzhEHT2L3KoWRKFq4eXe2WNfOu6oAsGp0r17hPxrD6thAWJSKl4ED6BFl6BsuczNl7rmNVWZTpSa99YRVgjjLP1njPhnEdZMEPh1dcc/s965/lens.jpeg"\; imageanchor="1"\; style="margin-left:\; 1em;\; margin-right:\; 1em;"><img\; border="0"\; data-original-height="237"\; data-original-width="965"\; height="158"\; src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgosZLEVSjiEvXwflDd5koI\_hSFfhJEHop0lANj1kdHLA2EjNPAmIj\_ioCd0Vx7qMDl9buOxYZCJtAM1qIe5Ma7QzhEHT2L3KoWRKFq4eXe2WNfOu6oAsGp0r17hPxrD6thAWJSKl4ED6BFl6BsuczNl7rmNVWZTpSa99YRVgjjLP1njPhnEdZMEPh1dcc/w640-h158/lens.jpeg"\; width="640"></a></div>a)\; Object\; at\; :\; Infinity}}{}$$

$$\frac{\mathrm{<span> \; \; Image\; at\; :\; Focus</span>}}{}$$

$$\frac{\mathrm{<span> \; \; Nature\; and\; size:\; Real\; and\; inverted, </span>}}{}$$

$$\frac{\mathrm{<br>}}{}$$

$$\frac{\mathrm{b) }}{}$$Object at : between 2F1 and F1

$$\frac{\mathrm{ \; \; Image\; at\; :\; Focus}}{}$$

$$\frac{\mathrm{ \; \; Nature\; and\; size:\; Real\; and\; inverted,\; diminished}}{}$$

$$\frac{\mathrm{<br>}}{}$$

$$\frac{\mathrm{Lens\; formulae: }}{}$$

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