Refraction at Plane Surface Formulas
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Refraction at Plane Surface Formulae Sheet
If c → Velocity of light in air
V → Velocity of light in a medium
µ → Absolute refractive index of medium.
µm → Permeability of medium.
εm → Permittivity of a medium.
µ0 → Permeability of free space.
∈0 → Permittivity of free space.
c = \(\frac{1}{\sqrt{\varepsilon_{0} \mu_{0}}}\), v = \(\frac{1}{\sqrt{\varepsilon_{m} \mu_{m}}}\)
┬╡ = \(\frac{c}{v}=\sqrt{\frac{\varepsilon_{m} \mu_{m}}{\varepsilon_{0} \mu_{0}}}=\sqrt{\varepsilon_{r} \mu_{r}}\)
refractive index of 2 w.r.t. 1
1┬╡2 = \(\frac{\mu_{2}}{\mu_{1}}=\frac{\mathrm{c} / \mathrm{v}_{2}}{\mathrm{c} / \mathrm{v}_{1}}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}\)
1. Laws of refraction
- Frequency (Colour) and phase not change (while wavelength and velocity changes) when light ray go from one medium to another medium.
- I, R & N are in a same plane.
- SnellΓÇÖs law \(\frac{\sin i}{\sin r}={ }_{1} \mu_{2}=\frac{\mu_{2}}{\mu_{1}}=\frac{v_{1}}{v_{2}}=\frac{\lambda_{1}}{\lambda_{2}}\)
2. Total internal reflection
It occur when i > ╬╕c (Critical angle) At ╬╕c, the refracted ray just grazes the boundary between two media.
sin ┬╡1╬╕c = ┬╡2 sin 90┬░
╬╕c = sin-1\(\frac{\mu_{2}}{\mu_{1}}\)
If ┬╡2 = 1 (air), ╬╕c = sin-1\(\left(\frac{1}{\mu}\right)\)
3. Brewester law
When partially reflected & refracted rays makes 90┬░ angle then both get polarised.
and ip = tan-1┬╡
4. Refraction by slab
Lateral displacement d
d = t \(\frac{\sin (i-r)}{\cos r}\)
In fig. I & II lines are parallel.
5. Apparent depth (Dapp)
dapp = \(\frac{\mathrm{d}_{1}}{\mu_{1}}+\frac{\mathrm{d}_{2}}{\mu_{2}}+\frac{\mathrm{d}_{3}}{\mu_{3}} \ldots \ldots \frac{\mathrm{d}_{\mathrm{n}}}{\mu_{\mathrm{n}}}\)
Apparent shift (s)
s = d – dapp
6. Equivalent ┬╡
┬╡ = \(\frac{d_{\text {actual }}}{d_{\text {app. }}}=\frac{d_{1}+d_{2} \ldots \ldots . d_{n}}{\frac{d_{1}}{\mu_{1}}+\frac{d_{2}}{\mu_{2}} \ldots \ldots . \frac{d_{n}}{\mu_{n}}}=\frac{d}{\sum_{i=1}^{i=n} \frac{d_{i}}{\mu_{i}}}\)
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