Refraction of Light at Plane Surfaces

just kill me already

Reflection of light

The return of light back in the same medium after striking a polished surface

Denser and rarer media

If, when entering a medium, light slows down, the second medium is said to be optically denser. If it speeds up, the second medium is optically rarer.

Refraction of light

The change in the direction of path of light when it passes from one transparent medium to another transparent medium, is called refraction. It is a surface phenomenon.

Partial refraction

When light passes from one medium to another, most of it may be refracted but some part is reflected, which is why reflected light is less intense than the incident light.

Denser to rarer medium

Light bends away from the normal

Rarer to denser medium

Light bends towards the normal

Light incident normally

Passes undeviated

Cause of refraction

Change in speed of light; when it slows down it bends towards normal and when it speeds up it bends away.

Laws of Refraction (Snell's Laws)

- The incident ray, refracted ray and normal at the point of incidence all lie in the same plane.
- The ratio of the sine of the angle of incidence i to the sine of the angle of refraction r is constant for the pair of given media (refractive index)

Refractive index

The refractive index of the second medium with respect to the first medium is the ratio of the sine of the angle of incidence in first medium to the sine of the angle of refraction in second medium.

Effect of refraction on frequency

Frequency of light does not change on refraction

Effect of refraction on wavelength

Rarer to denser -> speed decreases, wavelength decreases
Denser to rarer -> speed increases, wavelength increases.

Absolute refractive index

The ratio of the speed of light in vacuum to the speed of light in that medium

Wavelength in 2 media

Wavelength 2 = Wavelength 1 / Refractive index of that medium.

Factors affecting refractive index

- Nature of the medium
- Physical conditions such as temperature
- Wavelength or colour of light (refractive index of a medium decreases with increase in wavelength)

Reversibility of path of light

refractive index 1 * refractive index 2 = 1

sin i / sin r * sin r / sin i = 1

Refraction in rectangular glass block

Due to refraction of light in a parallel sided glass block, the angle of emergence is equal to the angle of incidence, and the emergent ray and incident ray are parallel, but they are not along the same line.

Lateral displacement

The perpendicular distance between the path of emergent ray and the direction of incident ray after travelling through the parallel sides of a rectangular glass block.

Factors affecting lateral displacement

- Thickness of medium - directly
- Angle of incidence - directly
- Refractive index - directly (wavelength - inversely)

Prism

A transparent medium bounded by 5 surfaces, with a triangular cross section. In each refraction, light bends towards the base of the prism.

Angle of deviation δ

δ = (i1 + i2) - (r1 + r2)

r1+r2 = angle of prism A.
i1 + i2 = A + δ.

Factors affecting angle of deviation δ

- angle of incidence
- material of prism
- angle of prism
- colour or wavelength of light

Dependence on angle of incidence

As the angle of incidence increases, the angle of deviation first decreases, reaches a minimum value for a certain angle of incidence, and on further increasing the angle of incidence the angle of deviation increases.

Position of minimum deviation

refracted ray is parallel to the base of the prism, δmin = 2i - A

Dependence on material of prism

Higher refractive index produces greater deviation

Dependence of deviation on angle of prism A

Directly proportional

Dependence on wavelength of light

Colours with lower wavelengths get deviated more.

Apparent depth

An object placed in an optically denser medium when viewed from a rarer medium appears to be at a depth lesser than its actual depth.

apparent depth = real depth/refractive index

Refractive index relation to real and apparent depth

ri = real depth / apparent depth

Critical angle

angle of incidence in the denser medium corresponding to which the angle of refraction in rarer medium is 90 degrees

Relation between refractive index and critical angle

refractive index = 1/sin C or cosec C

Critical angle of glass

42 degrees

Critical angle of water

49 degrees

Total Internal Reflection

When a ray of light travelling in a denser medium is incident on the surface of a rarer medium at an angle greater than the critical angle of the pair of media, the ray is totally reflected back into the denser medium.

TIR vs Reflection in plane mirror

TIR takes place only when light moves from a denser to rarer medium at an angle of incidence greater than the critical angle while Reflection from plane mirror does not depend on angle of incidence.

In TIR the entire energy is reflected while in Reflection from plane mirror only a part is reflected and the rest is refracted and absorbed

TIR image is much brighter as there is no loss of energy.