✤ OPTICS: The branch of Physics which deals with the study of nature i.e. Production & propagation of light.

                                                            OPTICS

                   RAY OPTICS                                                       WAVE OPTICS

           It is based on                                                  It is based on wave nature of light

                  1. rectilinear propagation of light.                        1) Interference

                  2. Reflection and refraction of light                      2) diffraction     3) Polarisation

✤ Reflection of light:

          i = angle of incident

          r = angle of reflection.

  ❄ If a ray strikes to the plane in normal direction then i = r = 0°

  ❄ Image by plane mirror is always virtual and erect, same size and laterally displaced.

  ❄ Focal length of plane mirror is infinite and power of plane mirror is zero.

✤ Pole :- If two plane mirror are placed at a angle of each other then no. of images formed are = 180/α

❈ SPHERICAL MIRRORS => Those mirror, which are the part of sphere.

                                                                        

            ✧ Some properties of concave mirror :                                                ✧ Some properties of convex mirror :

                                                                                    

                § Image formed by concave mirror                                                    § Image formed by Convex is always Virtual and erect, small in seize, b/w

                        is always real and inverted                                                            P and F for every position of ojbect.

                        (virtual and erect image)                                                           § It is called diverging mirror.

                § It is called converging mirror.

Mirror formula: It is the relation b/w f (focal length), u (distance of object) and v (distance of image).

Sign Convention:

             for concave mirror:                                    for covex mirror:

                 f = -ve                                                            f = +ve

                 u = -ve                                                            u = -ve

             v = -ve (Real image)                                            v = +ve

             v = +ve (virtual image)

Linear magnification: Ratio of height of image and height of object.

                                           m = -v/u

                                               or

                                           m=h₁/h₀

Note:        1) If m is +ve then image is Virtual and erect.

                2) If m is -ve then image is Real & inverted.

                3) If |m| > 1, magnified image

                4) If |m| < 1, diminished image

                5) If |m| = 1, same size.

Note: magnification m = f / (f-u) or m = (f-v) / f

✤ Try these!

        Q 1. If you are sit in a parked car, you glance in the rear view mirror R=2 m and notice a jogger approaching. If the jogger is running at a speed

               of 5 m/s, how fast is the image of jogger moving when the jogger is         (a) 9 m (b) 29 m (c) 19 m (d) 9 m away?

        Q2. A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length f such that its image which is real and elongated, just                touches the rod. What will be the magnification.

                ✤ Refractive index = Ratio of speed of light in one medium to another medium.

                                                          ‘μ₂ = V₁ / V2 ‘μ₁ = μ₂ / μ1

                                                    refractive index of 2nd w.r.t. 1.

                ✤ Lateral shift: It is the ⊥ distance b/w incident ray and emergent ray.

                                                    

                ✤ Normal shift: Difference b/w Real depth and apparent depth.

                                               Here μ = (Real Depth / apparent depth)

                                                        μ = y/x

                                                        

                                                and normal shift = y-x = y(1- 1/ μ)

                ✤ Critical angle: Angle in denser medium for which angle of refraction in rarer medium is 90°

                                                 Here Ic is called critical angle.

                                                                                

                                                 Here μ = 1/sin ic

                ✤ Total internal reflection (TIR): The phenomenon of bouncing back of light in same medium, when light                                                                       travel from denser to rarer.

                                                                            

                ✤ Conditions for TIR: 1. Light showed travel from denser to rarer medium.

                                                    2. Angle of incidence in denser medium is greater than the critical angle.

            1. Totally reflecting Prism! These are right angle isosceles prim.

            2. OPTICAL fibre: It is a hair hair thin long

                                             • Strand of quality glass surrounded by a glass coating of less refractive index.

            3. If a light bulb is placed at bottom of a pool

                          1. radius of circle of Light =  h/√(μ² - 1)

                          2. area = πh² / μ²-1

                          3. diameter 2h / √(μ² - 1)

        ❈ Convex lens:      1. It is thick in middle.

                                       2. It makes Real and inverted image.

                                            except when object is placed b/w o and f.

                                                    (virtual and erect)

                                       3. It is also called converging lens.

        ❈ behaviour of Convex :→

        ❈ Some terms related to concave: → 1. It is thick at corner.

                                                                     2. It always makes virtual and erect image.

                                                                     3. It is called diverging.

                            

        ❈ Refraction by a convex refracting surfaces

                            

                             μ₂-μ₁/R = μ₂/v - μ₁/u

                                 (for real image)

        ❈ Some important note : -

                  1. for convex and concave, formula is same but you should use proper sign.

                  2. for rarer to denser μ₂-μ₁/R = μ₂/v - μ₁/u

                  3. for denser to rarer μ₁-μ₁/R = μ₂/v - μ₁/u

                  4. If rarer medium is air then [μ₁ = 1]

                  5. for an object is placed in air μ/R = μ/v - 1/u

                  6. Here μ₂-μ₁/R is called Power factor. It describe the degree of converge or diverge.

                  7. f₁ = - μ₁R/μ₂-μ₁ , f₂ = μ₂R/μ₂-μ₁

              

          If refractive index of glass = µ₂

          If refractive index of medium = µ₁

          then 1/f = (μ-1) (1/R1 – 1/R2)                          Here μ = µ₂/µ₁

          ❈ If refractive index of air is µ₁ = 1 then

          Note:      1. for equi-convex lens R₁ = R。

                                                              R₂ = -R。 but R₁ = -R。

                                                                              (in Numerical)

                          2. Radio of focal length in two media

                                     Fw / Fg = (aμg-1) / (wμg-1)

                          3. for plano-convex R₁ = R

                                         R₂ = ∞

                          4. If lens is cut then focal length of New lens = 2f

✤ Power of lens: Converging or diverging ability of a lens.

                                 P = 1/f(m) unit is dioptre (D)

                                    ❅ Power of convex lens is +Ve

                                    ❅ Power of concave is -Ve.

✤ Power of combination of two or more lens:

               Total power is equal to the algebraic sum of their individual power.

                         P = P₁ + P₂ + …....... Pₙ

       ✥ If two lens are placed separated by small distance d

                Focal length of convex lens at a distance position = D²-d²/4D

                 B - dist b/w screen & pole

                 d – distance b/w 2 concave lens

                    1/f = 1/f₁ + 1/f₂ - d/f₁f₂

✤ PRISM :→

          It is a wedge shaped portion of a transparent refracting medium.

          δ(angle of deviation): Angle b/w incident ray and emergent ray.

                      1. δ = (i₁+i₂) - (r₁+r₂)

                      2. Here r₁+r₂ = A

                      3. δ = (µ-1) A

                      4. for minimum deviation i₁=i₂ and r₁=r₂

                      5. r= A/2 {r=s]

                                    and δmin = 2i-A

                      6. Refractive index μ = sin ((Sm+A)/2) / sin (A/2)

✩ Some important fact about angle of deviation:→

          1. δ depend upon angle of incidence.

          2. δ depend upon material of the Prism

          3. δ depend upon the wave length of light and.

          4. δ depend upon Angle of Prism (A)

✤ Variation of δ with i

            Note:     1. deviation produced by Prism is maximum when i=90

                          2. for small angle of Prism (A), 8=(μ-1)A, for larger angle

                                             δ=μ₁₁ +μ₂ -A

                          3. There is only ane angle of incidence for which deviation is minimum

                          4. for a Prism 8 = (μ-1) A, does not depend upon angle of incidence.

✤ Dispersion of light: The phenomenon of splitting of white light into its seven colours.

❆ Cause: main cause is μα 1/λ (change in wavelength)

                      Note: Refractive index of yellow light My = μ₁+μ₂/2

             So yellow is called mean light and its deviation is called mean deviation.

             ❆ due to small wave length violet light is harmful to our eye.

Q. A ray of light PQ is incident at angle of 60° on the face AB of Prism's angle 30°. The ray emerging out of the Prism makes an angle 30° with incident ray.     Show that emergent ray is ⊥ to BC.

Q.

          find 1) refractive index

          2) draw the path of emergent ray.

❈ Compound microscope:→ It is an optical instrument by which we can see magnified images of tiny objects. magnification is about 1000 times of object.

❈ Magnifying Power: m = tanβ → angle made by image

                                   (tanα) ̅ → Angle made by object.

                          or m = mo x me → magnifying Power of eye piece

                                       ↓

                     magnifing Power of objective

                               Here mo = Vo / |uo| and me = 1+ D/fe

                               Here D = 25 cm

                Note: If object is placed very close to objective

                           Then uo = - fo and Vo = L (length of tube)

                Note:      1. When final image at infinite: mo = -L/fO , me =D/fe

                               2. Length of tube L = fo+ve

                               3. length of tube when final image at least distance

                               4. We can arrange position of objective L = Vo+Ue and eye piece by rack and Pinjon method.

                               5. fe > fo to increase area of view when Image formed at infinity

                                              m = mo x me

                                                  = -L/fo X D/fe    

✤ Astronomical telescope:→ It is an optical instrument by which we can see distant heavenly body like stars, planets etc.

✤ Magnifying Power: It is defined as the ratio of angle subtended at eye by final image formed at least distance to the angle subtended at the eye by                                     object at infinity.

                                                m = β/α

                                            m = -fo/fe (1+fe/D)

                                    when final image at infinite m = -fo/fe

✤ Some Imp terms

          1. objective lens have large focal length and large aperture but eye piece has small focal length and small aperture.

          2. distance b/w objective and eye lens   L = fo+fe. When image formed at infinity     VO = FO

          3. If makes an inverted image. As celestial objects are oval in shape, so it does not matter whether the final image is inverted or erect.

✤ REVISION

            1. mirror formula 1/f = 1/v + 1/u

 10. for refraction from rarer to denser medium           μ2/V – μ1/u = μ2- μ1/R

 14. when lens is placed in air, μ₁=1              1/f = (μ- 1)/ μ1 (1/R1 – 1/R2)