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Waves, Light and Quanta (Reflection and Refraction, Snell's law…
Waves, Light and Quanta
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Huygens construction
Every point of the wavefront is a source of secondary spherical wavelets which spread out at the wave speed
The wavefront at a later time is the surface tangent to all the wavelets in the forward direction, called the enelope of the wavelets
Reflection and Refraction, Snell's law
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Total internal reflection (\(n_i > n_t \)): \( \sin \theta_{i, \text { crit }}=\frac{n_{t}}{n_{i}} \)
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Ray tracing
A ray leaving the object parallel to the axis is refracted to pass through the focus on the image side
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A ray passing through the centre of the lens (i.e. on axis when it goes through the lens) is undeflected.
Matrix formulation
Ray specified by : \( \left( \begin{array}{l}{y} \ {\alpha}\end{array}\right) \quad \begin{array}{l}{\text { distance from axis }} \ {\text { slope (angle) to axis }}\end{array} \)
OPtical element represented by a matrix acting on rays: \( \left( \begin{array}{l}{y^{\prime}} \ {\alpha^{\prime}}\end{array}\right)=\left( \begin{array}{ll}{A} & {B} \ {C} & {D}\end{array}\right) \left( \begin{array}{l}{y} \ {\alpha}\end{array}\right) \)
Chain of optical elements represented by product of corresponding matrices : \( \left( \begin{array}{l}{y^{\prime}} \ {\alpha^{\prime}}\end{array}\right)=M_{3} M_{2} M_{1} \left( \begin{array}{l}{y} \ {\alpha}\end{array}\right) \)
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Magnification
Lateral Magnification: \( \frac{\text { lateral size of image }}{\text { lateral size of object }} \)
Angular Magnification : \( \frac{\text { angle subtended by image }}{\text { angle subtended by object }} \)
For magnifier or microscope, in the denominator conventionally use the angle subtended by the object when viewed at the near point (25 cm) by the unaided eye
Magnifier
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Bottom: object brought close to the lens so that the image distance corresponds to the eye's near point when the eye is close to the lens
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Refracting telescope
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Assume virtual image at infinity, hence parallel outgoing rays
