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### Optics : Light

Laws of Reflection

#### Magnification

The magnification (lateral, transverse or linear) magnigication is defined by

$M ={ \textrm{height of image} \over \textrm{height of object} } = { \textrm{image distance} \over \textrm{ object distance} }$

#### Refraction of Plane surface

The phenomenon of bending light passes from one medium to another medium is called refraction.
The Frequency remain unchange during refraction
The perpendicular distance between the direction of incident ray and emergent ray called the lateral shift.

Law of Refraction

• The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
• The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction.

${ sini \over sinr } = η$

Refraction Index Relationship

i) 1η2 = \( { 1 \over 2η1 })\
ii)

Real Depth and Apparent Depth

μ = $\textrm{ real depth }\over \textrm{apparent depth}$ if the object is inside and observer is outside the medium
μ = $\textrm{ apparent }\over \textrm{real depth}$
Apparent Shift (diffrence in real depth and apparent depth) : d = $({1 - {1 \over μ }}) t$
When several slabs of thickness t1, t2 ... and refractive indices μ1, μ2... are placed on one above another, the apparent depth is given as ta = $t1 \over μ1$ + $t2 \over μ2 + ....$

Lateral Shift

$d = { t sin(i -r) \over cosr }$ The perpendicular distance between the incident ray and emergent ray when light incident obliquely on a parallel sided slab of refracting materical is called lateral shift Lateral Shift depends on the nature of material of the slab, thickness of the slab and angle of incidence

### Refraction through Lenses

The Lens formula

${1 \over f} = {1 \over u } + {1 \over v}$

Lens Maker Formula
${1 \over f} = (μ - 1)({1 \over R_1 } + { 1 \over R_2 })$
μ is the refractive index of the material with respect to the medium outside it.

The Power of lens is given by
P = ${ 1 \over f}$
f is in meter

Myopia or short sightedness

• myopic eye can see near clearly but cannot see distance object clearly
• It can be removed by the use of concave lens whose focal length lens whose focal length is equal to far point of myopic eye
• Image of distance object is formed infront of the retina

Hypermetropia of long sightedness

• A hypermetropia or long sightedness can see distance object clearly but not nearer objects
• It is caused due to increase in focal length of eye lens or due to contraction of eye ball
• Image of distance object is formed behind the retina
• It can be removed using convex lens

Magnification

$m = { v \over u } = { I \over O } = {v - f \over f} = {f \over u - f}$

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