CBSE Class 10 Science Notes - Light: Reflection and Refraction PDF

# Light: Reflection and Refraction ## Light: - The form of energy which gives sensation of sight to our eyes is called light. - The form of energy which makes anybody visible but it is itself invisible is called light. ## Properties of Light: 1. Light is a form of energy which does not require any...

# Light: Reflection and Refraction ## Light: - The form of energy which gives sensation of sight to our eyes is called light. - The form of energy which makes anybody visible but it is itself invisible is called light. ## Properties of Light: 1. Light is a form of energy which does not require any medium to travel. 2. Light travels on a straight path. 3. Light travels fastest in vacuum. It's speed is 3 x 10⁸ m/s. 4. The wavelength of visible light is 400nm - 700nm. 5. Light consists of small packets of energy called photons. ## Sources of Light: 1. **Natural Source**: Stars, sun, firefly, fire, etc. 2. **Artificial Source**: Torch, electric bulb, tubelight, etc. 3. **Hot source of light**: Sun, fire, lamp, candle, etc. 4. **Cold source of light**: Stars, firefly, LED, etc. ## Types of object based on production of light: 1. **Luminous Object**: The object which has its own light is called luminous object. 2. **Non-Luminous object**: The object which doesn't have its own light is called non- luminous object. ## Types of object based on propagation of light: 1. **Transparent**: The object which allows whole light to pass through it is called transparent. e.g., glass, air, water. 2. **Opaque**: The object which doesn't allows light to pass through it is opaque. e.g., wood. 3. **Translucent**: The object through which light passes partially is called translucent. e.g., rubbed glass, oily paper, etc. - **Ray**: Path of light is called **ray**. - **Beam**: Group of rays of light is called **beam**. - |---|---| |Parallel beam| } | ## Reflection of Light: - Bouncing back of light after striking the surface is called reflection of light. - **Types of reflection of light**: 1. **Regular reflection of light**: Reflection of light occurs due to smooth and shiny surface. 2. **Irregular reflection of light**: Reflection of light occurs due to rough surface. **Note:** - Due to regular reflection of light, image is formed. - Due to irregular reflection of light, we are able to read newspaper and book. ## Mirror: - The smooth and shiny surface which causes regular reflection of light to form image of an object is called mirror. - **Classification of mirror**: - |---|---| |Plane mirror| Mirror | Spherical mirror | | |Concave||| Convex ||| **Plane mirror**: The mirror whose reflecting surface is plane is called plane mirror. ## Laws of reflection of light: 1. Incident ray, reflected ray and normal at the point of incidence all together lie in the same plane. 2. Angle of incidence = Angle of reflection. [∠i = ∠r] **According to law [∠i = ∠r]** - **Image:** Rays of light coming from a point object intersects or seems to intersect each other at a point after reflection from mirror, then the point is called image of that point object. - **Types of image**: 1. **Real image**: Rays of light coming from a point object intersects each other at a point after reflection from mirror then the point is called real image of the point object. 2. **Virtual image**: Rays of light coming from a point seems to be intersect each other at a point of int. after reflection from mirror, then the point is called virtual image of the point object. **Note:** - Real image is invested. - Virtual image is erect. ## Properties of image formed in plane mirror: 1. Image is virtual and lateral inverted. Left appears right and right appears left is called lateral inversion. 2. Height of the image is equal to height of the object. 3. Distance of the image from the mirror is equal to distance of the object from the mirror. 4. If the object is at distance ‘d’ from the mirror then is image will appear at distance 2d. 5. If a person is moving with the speed ‘v’ in front of the mirror then he will observe his image moving with speed 2v. ## No. of images formed with two plane mirrors: - When two plane mirrors are placed at an angle θ' such that their reflecting surfaces face each other, then total number of images (n) formed is given by: - **No. of images = 360°, when the ratio is odd number.** - **No. of images = 360°-1, when the ratio is even number.** - In case of decimal no. integeral part refer to the number of image. ## Velocity Problems 1. When we have to find speed of image with respect to mirror. [v=u] - The image is moving with respect to the mirror, so the velocity is u. - **v=u** 2. To find speed of image with respect to object. [v=2u] - The image is moving with respect to the object, and the object is at rest, so the velocity of the image is twice the velocity u. - **v=2u** 3. To find speed of image when mirror starts moving towards the object. [image velocity = u] - The image is moving towards the object, but the object is still at rest, so the velocity is u. - **image velocity = u** ## Spherical Mirror: - The curved reflecting surface which is a part of hollow sphere of glass is called spherical mirror. - There are two types of the spherical mirror: 1. **Concave Mirror**: The spherical mirror whose inner surface is reflecting surface is called concave mirror. 2. **Convex Mirror**: The spherical mirror whose outer surface is reflecting surface is called convex mirror. **Note:** - Concave mirror is also known as converging mirror. - Convex mirror is also known as diverging mirror. **In concave mirror both real and virtual image may be formed.** **In convex mirror only virtual image is formed.** ## Some defining terms in spherical mirror: 1. **Pole**: Centre of the mirror is called pole. It is denoted by **P**. 2. **Centre of Curvature** Centre of sphere whose mirror is a part of is called centre of curvature. It is denoted by **C**. 3. **Principal axis:** The straight line passing through pole and centre of curvature is called principal axis. 4. **Focus:** The point on the principal axis where all the paraxial rays meet or seems to meet after reflection from mirror is called **focus**. 5. **Focal length: ** Distance from Pole to focus of the mirror is called focal length. It is denoted by **f**. 6. **Radius of Curvature:** The distance from pole to centre of curvature is called radius of curvature. It is denoted by **R**. 7. **Aperture:** Width of the mirror is called **aperture**. 8. **Aberration:** The defect of mirror due to which some paraxial ray doesn't meet at focus after reflection. ## Prove that R = 2f: - In concave mirror, Let there be concave mirror of focal length ‘f’ and radius of curvature ‘R’. Light AB incidents at point B, which passes through focus after reflection from mirror. - A line is drawn from C to B which will be normal to the mirror. - In the figure, ∠ABC = ∠CBF. - AB||PC and BC is a transversal line. Therefore, ∠ABC = ∠BCF [alt. int. ∠s] - From equation 1 and 2, ∠CBF = ∠B C F - In ΔBCF, ∠BCF =∠CBF - If the mirror is of small aperture then, point B would be closer to point P. Therefore, FC = PF. - Now, in mirror, PC = PF + FC. Therefore, PC = PF + PF, PC = 2PF. - On putting PC = R & PF = f, R = 2f ## Rules of reflection of light to trace the image formation: 1. **Ray of light which is parallel to the axis passes through focus after reflection from mirror.** 2. **Ray of light passing through focus moves parallel to axis after reflection from mirror.** 3. **Ray of light which is passing through centre of curvature returns on the same path after reflection from mirror.** 4. **Ray of light which incident on pole, it reflects obliquely.** 5. **Positions of object before concave mirror**: - |---|---|---| |Object|Image|Nature| | ∞ | ∞ | Real | | C| Behind C & ∞|Real| | Between C & F | Between C & F|Real| | Between C & ∞ | Between C & F| Virtual| | Between P & F | Bt Behind the mirror | Virtual | ## Image formation in concave mirror: 1. **When the object is between P and F:** In this case, virtual and erect image is formed behind the mirror. Size of the image is larger than that of the object. 2. **When the object is at focus**: In this case, real and inverted image is formed at infinity. Image is highly enlarged. 3. **When object is between C & F**: In this case, real and inverted image is formed beyond C. Image is larger than that of the object. 4. **When the object is at C**: In this case, real and invested image formed at c. 5. **When the object at beyond c**: In this case, real and invested image is formed between C & F. Image is smaller than object. 6. **When the object is at infinity**: In this case, real and invested image is formed at f. ## Sign Convention in mirror: 1. Object is always placed left to the mirror. 2. All the distances in the mirror are measured from pole. 3. The distance measured left to the pole is negative and distance measured right to the pole is positive. 4. The distance measured above the principal axis is positive and below the principal axis is negative. ## In Convex lens - The image is formed at F. - The focal length is negative. - The radius of curvature is negative. ## Sign convention may be remembered with the help of table given below: - |Mirror|U|V|f| - |---|---|---|---| - |Concave|-|-(Real)/(Virtual)|- | - |Convex| -|+|+| ## Derivation of mirror formula in concave mirror: - In the figure, AM||BP and MNLBP. Therefore, MN=AB - Now, ΔABE ~ ΔA'B'C. Therefore, AB/A'B' = BC/B'C - Similarly, AMNF~ΔA'B'F. Therefore, MN/A'B' = NF/B'F - AB/A'B' = NF/ B'F = [MN=AB] - If the mirror is thin then point N would be closer at point P'. In this case, NF = PF. Therefore, AB/A'B' = PF/B'F - From equation 1 and 2, BC/B'C = PF/B'F - PC-PB' = PF/PB-PF - From sign convention, PB=-u, PC=-R=-2f, PB’=-v. - On putting these values in equation 3, (-u)-(-2f) = (-f)/(-v)-(-f) - -u+2f = -f/-2f+v - uv - uf -2vf +2f² = 2f² - vf - uv - uf - 2vf + vf = 0 - uv - uf - vf = 0 - Dividing by uvf both the sides, we get, uv/uvf - uf/uvf - vf/uvf = 0/uvf - 1/f + 1/v = 1/u ## Magnification: - The ratio of height of image (h₂) to height of object (h₁) is called magnification - [m=h₂/h₁] - OR - Magnification = height of image/height of object. - **Note:** - Magnification has no unit. - For real image, m=-ve - For virtual image, m=+ve - In the figure, ΔABP~ΔA'B'P. Therefore, AB/A'B' = PB/PB' - Using sign convention, -h₁/h₂ = -V/ -u - Therefore, h₁= -v/u - Therefore, h₂ = -v - Therefore, h₂/h₁ = -v/u - m = -v/u. - From missos Formula, 1/v + 1/u = 1/f - Multipling by v both the sides, v/v + u/u = v/f - v/u + 1 = v/f - v/u = v/f - 1 - v/u = v-f/f - -v = v-f/f - m = 1-f/f - m = f- v/f - By multiplying by u both the sides, u/u + v/u = u/f - 1 + v/u = u/f - v/u = u/f - 1 - v/u = u-f/f - -v = u-f/f - m = f-u/f ## Refraction of light: - Deviation of light from its real path while changing the medium is called refraction of light. - **Optical medium:** The medium light passes through which is called optical medium. - There are two types of medium, rarer & denser medium. - **Note:** Water is denser than air but it is rarer than glass. ## Different media and velocity of light: - | Medium | Velocity | - |---|---| - | Vacuum | 3 x 10⁸ m/s | - | Air | 3 x 10⁸ m/s | - | Water | 2.25 x 10⁸ m/s | - | Glass | 2 x 10⁸ m/s | ## Deviation of light while changing the medium: 1. **When light moves from rarer to denser medium, then refracted ray moves towards the normal.** - [i > r] 2. **When light moves from denser to rarer medium then reflected ray bends away from the normal.** - [i < r] 3. **Refraction of light due to glass slab:** - **Here:** - PQ = Incident ray - QR = Refracted ray - RS = Emergent ray - **i** = ∠ of incidence - **r₁** = ∠ of refraction - **e** = ∠ of emergence - **d** = Lateral displacement 4. **Refraction of light due to prism:** - **S** = ∠ of deviation/ dispersion ## Laws of Refraction of light: 1. Incident ray, refracted ray and normal all together lie in the same plane. 2. For any colour of light the ratio of sine of angle of incidence (sin **i**) to sine of angle of refraction (sin **r**) is constant. This law is also known as **Snell's law**. - According to the law, [sin **i** / sin **r** = constant] or [sin **i** / sin **r** = **n**] - Here, **n** is a constant and also known as **refractive index.** ## Refractive Index: - The ratio of velocity of light in vacuum (c) to velocity of light in a medium is called **refractive index** of that medium or **absolute refractive index** of that medium. - **Refractive index of medium** - [**n_m** = c/v_m] - **e.g.** - **Refractive index of water:** - **n_w** = c/v_w - = 3 x 10⁸ m/s / 2.25 x 10⁸ m/s - = 300 / 225 - = 1.33 - .. [**n_w** = 1.33] - **Refractive index of glass:** - **n_g** = c/v_g - = 3 x 10⁸ m/s / 2 x 10⁸ m/s - = 3/2 - = 1.5 - .. [**n_g** = 1.5] **Note:** - Refractive index has no units. - Refractive index of air is 1.0003. - Refractive index of diamond is 2.42 - As the medium becomes denser the value of refractive index increases. ## Relative refractive Index: - The ratio of velocity of light of the two media is called **relative refractive index.** - Refractive medium of the first medium with the second, [n₂₁ = v₂/ v₁] - Similarly, [n₂₁ = v₁/ v₂] ## Relation between refractive index and velocity of light in medium: - From Snell's law, n₂ = v₁/v₂ = c/v₂ / c/v₁ = n₂/n₁ - .. [n₂ = v₁/v₂ = n₂/n₁] - .. [v α 1/n] - **Note:** As the medium becomes denser, then refractive index increases. ## Important formula: - v₁ x v₂ = 1 - n₂ x v₂ = 1 .. [n₂ = 1/v₂] ## To prove that refracted ray of light bends towards the normal when light moves from rarer to denser: - Let there be 2 media of refractive indices, n₁ & n₂. Light moves from the first medium to second medium. - Applying Snell's law, n₂ = sin i/ sin r ... (1) - & n₂ = n₁/n₁ = r/r ..(2) - From equation 1 and 2, sin i/ sin r = n₂/n₁ - If the 1st medium is rarer in comparison to the second, then, n₂ > n₁. - .. n₂/n₁ > 1 ..(4) - Now, from equation 3 and 4, sin i/ sin r > 1 - sin i > sin r - .. [i > r] ## To prove **i** = **e** in a glass slab - Let there be a glass slab of refractive index of n_g is kept in the air medium of refractive index n_a. - **Applying Snell's law, when light moves from air to glass:** - n_g/n_a = sin i/ sin r₁ ...(1) - & n_g/n_a = sin r₂/ sin e ...(2) - **From equation 1 and 2:** - sin i/ sin r₁ = sin r₂/ sin e ...(3) - **Applying Snell's law, when light moves from glass to air:** - n_a/n_g = sin r₂/ sin e ...(4) - & n_a/n_g = sin e / sin r₁ ...(5) - **From equation 4 and 5:** - sin r₂/ sin e = sin e / sin r₁ ....(6) - **From equation 3 and 6:** - sin i/ sin r₁ = sin r₂/ sin e - **In the figure, normals are parallel to each other.** Therefore, sin **r₁** = sin **r₂** [alt. int. ∠s] - .. sin **i** = sin **e** [from equation 6] - .. [**i** = **e** ] ## Critical angle (C): - The angle of incidence for which angle of refraction is equal to right angle is called critical angle. [n₁ > n₂] ## Total internal reflection (TIR): - When light moves from highly denser to highly rarer medium and θ becomes greater than right angle, this phenomenon is called **total internal reflection**. Diamonds shines due to TIR. ## [Refractive index = real depth/ apparent depth] ## Two cases for refraction of light without deviation: 1. **When light incidents normally at the separating surface:** - Let there be two media having refractive indices n₁ & n₂. Light moves from the first medium to the second. - Applying Snell's formula, here, n₂ = sin i/ sin r ...(1) - & n₂ = n₂/ n₁... (2) - From equation 1 and 2, sin i/ sin r = n₂/ n₁ - sin i/ sin r = n₂/n₁ ... (3) - If lights incidents normally then i = 0. Therefore, sin i = sin 0^o = 0 - From equation 3, sin r = n₁/n₂ * 0 - sin r = 0 - sin r = sin 0^o - .. r = 0^o - .. [i = r] 2. **When the medium remains same:** - Let there be two media having refractive indices n₁ & n₂. Light moves from the first medium to the second. - Applying Snell's law formula, n₂ = sin **i** / sin **r** ...(1) - & n₂ = n₂/n₁ ... (2) - From equation 1 & 2, sin **i** / sin **r** = n₂/n₁ - sin **i** / sin **r** = n₂/n₁ ... (3) - If the medium remains same, then, n₂=n₁. Therefore, n₂/n₁ = 1 - From equation 3, sin **r** = 1 x sin **i** - sin **r** = sin **i** - .. [ **r** = **i** ] ## Lens: - The transparent substance whose atleast one surface is geometrical curve is called **lens**. - **Types of lens:** - 1 **Convex lens**: The lens whose middle part is thick and ends are thin is called **convex lens**. - 2 **Concave lens**: The lens whose middle part is thin and ends are thick is called **concave lens**. **Note:** - Convex lens is also known as **converging lens**. - Concave lens is also known as **diverging lens**. ## Terms related to lens: 1. **Optical centre (O):** The midnight of the lens lying on the axis, light passes through which, without any deviation is called optical centre. 2. **Focus:** The point on the principal axis where all paraxial rays meet or seem to meet after refraction due to lens is called focus. In the lens there are two foci. 3. **Focal length:** The distance from optical centre to focus of a lens is called focal length. 4. **Aperture:** Diameter of the circular edge of the lens is called as its aperture. ## Rules of refraction of light for image formation for lens: 1. **Ray of light passing through optical centre is not deviated.** 2. **Ray of light which is parallel to the lens, passes through focus after refraction due to lens.** ## Image formation in convex lens 1. **When the object is between lens and focus:** In this case virtual erect image is formed in the same side of the object image is larger than the object. 2. **When the object is at infinity**: Refer to book ## Sign Convention in lens: 1. The object is always placed left to the lens. 2. All the distances in the lens is measured from optical centre. 3. The distance measured right to the optical centre is positive and left to the optical centre is negative. 4. The distance measured above the principal axis is positive and below the principal axis is negative. ## In convex lens: - The principal axis lies between 2F and F - The focal length is positive. - The radius of curvature is positive. ## Sign convention can be remembered with the help of table given below: - |Lens|U|V|f| - |---|---|---|---| - |Convex| -|-| +| - |Concave|-|-|-| ## Lens Formula (from concave lens): - Let there be a concave lens of focal length ‘f’. An object AB is situated before the lens whose virtual and erect image A’B’ is formed in same side of the object from lens. - In the figure, AL||BO & LOLBO. Therefore, LO = AB. - Now, ΔABO and ΔA’B’O. Therefore, AB/A’B’ = OB/OB’ - Similarly, ΔLOF ~ ΔA’B’F’. Therefore, LO/A’B’ = OF/B’F’ - AB/A’B’ = OF/B’F’ ... (1) - From equation 1 & 2, OB / OB’ = OF/B’F’ - OB/OB’ = OF-OB/B’F’ …(3) - On putting sign convention in the above result: -u/-v = -f/-f-(-v) - -v/u = -f/-f + v - -uf + uv + vf = 0 - -uf/uvf + uv/uvf + vf/uvf = 0/uvf - -1/f + 1/v + 1/u = 0 - [1/f = 1/v + 1/u] ## Magnification: - The ratio of height of image to height of object is called magnification. - [m=h_i/h_o] - From the figure, which was drawn in the derivation of lens formula, ΔABO~ΔA’B’O. - Therefore, AB/A’B’ = OB/OB’ - On putting sign convention, h_o/v = h_i/u. - Therefore, h_i/h_o = v/u - [m=v/u] ## Power of lens: - Reciprocal of the focal length of the lens is called power of lens. - [ P = 1/f(mm)] or [P = 100 / f(in cm)] - **Note:** - SI unit of power of lens is dioptre(D). - For convex lens, P= +ve. - For concave lens, P=-ve. ## Power of combination of lenses - Resultant power of combination of lenses is equal to the algebraic sum of power of the lenses. - [P = P₁ + P₂]