## Chapter : 9

## What are Ray Optics and Optical Instruments ?

**Topic**

**Apparent Depth**

**Formula**

Apparent depth

= (real dept/µ)

**Symbol Representation**

µ=refractive index

=(sin i/sin r)(Snell's law)

i = incident angle of ray

r = angle of refraction

**Important Points**

When we look into a pool of water,

the bottom of the pool will appear to be raised due to refraction of light.

**Critical Angle**

^{-1}(1/µ) or μ = (1/sin c)

μ = refractive index of denser medium w.r.t. rarer medium

c = critical angle which depends on colour of light

Phenomenon of refraction of light

into denser medium from the boundary of denser medium with rarer medium known as total internal reflections

_{c}

Some of the important applications

of total internal reflection:

(a) Diamond brilliance

(b) Optical fiber

(c) Mirage

**Lens Maker’s****Formula**

_{1})-(1/R

_{2}))

μ = refractive index of material of lens w.r.t. medium in which lens is placed.

_{1}, R

_{2}= radii of curvature of the two surfaces of the lens.

This formula is valid for all

types of lenses.

**Thin Lens****Formula**

(1/v)-(1/u) =( 1/f)

u = distance of the object from the optical centre of the lens

v = distance of image from the optical centre of the lens

f = focal length of the lens

f is positive for converging or convex lens and negative for diverging or concave lens.

**Linear ****Magnification **

m=(I/O)-(V/U)

v = size of image

u = size of object

m is positive for virtual image and m is negative for real image.

Topic | Formula | Symbol Representation | Important Points |

Power of a Lens |
P = (1/f) | f = focal length in metres Unit of power of lens = dioptre = 1D = 1m ^{-1} |
• Ability of lens to converge or diverge a beam of light. • P is positive for a convex lens and negative for a concave lens. • When focal length of a lens is in cm, then P =(100/f(in cm))dioptre |

Combination of then lenses |
•(1/F_{1})+(1/F_{2})+(1/F)• P = P _{1} + P_{2}• m = m _{1} × m_{2} |
F_{1}, F_{2} = Focal length of two thin lenses places coaxiallyF = focal length of combination P = Power of lens with proper sign m _{1}, m_{2} = magnification |
Combination of lens used for: • Increase the magnification of image • Make the final image erract w.r.t. object • Reduce certain observations |

Angle of deviation |
δ = i_{1} + i_{2} – A |
i_{1} = angle of incidencei _{2} = angle of emergenceA = r _{1} + r_{2} = angle of prism |
The difference between the sum of incident angles and the sum of emergent angles is known as the angle of deviation. |

Prism Formula |
μ = sin[(A+δ_{m})/2]/sin(A/2)(Snell’s law) |
A = angle of prism δ _{m}= angle of minimum deviationi = angle of incidence δ _{m} = 2 i – Awhen i _{1} = i_{2}and r _{1} = r_{2} |
• For thin prism, Sin [A+δ _{m}]/2→(A+δ_{m}/2) and Sin (A/2)→(A/2)• δ = (μ–1)A this is the formula of angle of maximum deviation. |

Angular Dispersion |
θ = δ_{V} – δ_{R}= (µ _{V} – μ_{R}) A |
δ_{V}, δ_{R} = Deviation of violet and red lightμ _{V}, μ_{R} = Refractive index for violet and Red colour. |
The difference in the angle of deviation between two extreme colours is known as angle of dispersion or angular dispersion for the two colours. |

Magnifying Power of Simple Microsope |
• Image, at the least distance of vision m=1+(D/f) • Image at infinity m=(D/f) |
m = magnification D = least distance vision |
A simple microscope or a simple magnifying glass is a converging lens of small focal length. |

Magnifying Power of Compound Microscope |
• Image, at infinity m=(-L/v _{0}(D/f_{e}))• Image, at the least distance of vision m =(-V _{o}/U_{o}(1+(D/f_{e})) |
u_{o} = distance of object from the objective lensv _{o}=L=distance of image from the objective lens (length
of microscope tube)f _{e} = focal length of the eye lensD = least distace of distinct vision. |
• Compound microscope is the combination of two convex lenses one compounding the effect of the other, for much larger magnification. • The objective have smaller aperture and smaller focal length than the eye-piece. |

Topic | Formula | Symbol Representation | Important Points |

Mirror Formula |
(1/u)+(1/v)=(1/f) | u = distance of object from the pole of the mirror v = distance of image f = (R/2) |
• Mirror formula is same for both concave and convex mirrors equation remain uneffected whether the image is real or virtual. |

Linear Magnification |
• m =(size of image (h_{2})/size of object (h_{1}))• m =(f/f-v) |
f = focal length of magnifying lens. | In case of concave mirror, when image is real, m = negative. When image is virtual, m is positive. |

Use of spherical mirror |
• As reflector in street lamps, search light. • Driving mirror • Telescopes, solar cookers |
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Optical fiber |
• Based on total internal reflection. • Use for data transmission using light pulses. • Made of plastic or glass. |
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Magnifying Power Astronomical Telescope (Refracting Type) |
• When the final image is formed at infinity (Normal Adjustment), m=(f _{o}/f_{e})• When the final image is formed at least distance of distinct vision, m =(-f _{o}/f_{e})(1+(f_{e}/D)) |
f_{o} = Focal length of objective lensf _{e} = Focal length of the eye-pieceD = least distance of distinct vision (i.e. 25 cm) |
• Astronomic telescope (Refracting type) is consist of two converging lense the objective lens has large focal length and large aperture than the eye-piece. |

Magnifying Power of Reflecting Type Telescope |
In normal adjustment m =(-f _{o}/f_{e})=((R/2)/f_{e}) |
R = radius of curvature of concave mirror | • It is improvement over refracting type telescope. Here, the objective lens is replaced by a concave parabolic mirror. |