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Physics · 2023 · 3 marks
CBSE 2023 · Region 5 · Set 1 · Q26
(a) A plane wave-front propagating in a medium of refractive index ' μ_1 ' is incident on a plane surface making an angle of incidence (i). It enters…
(a)
A plane wave-front propagating in a medium of refractive index ' $\displaystyle \mu_{1}$ ' is incident on a plane surface making an angle of incidence (i). It enters into a medium of refractive index $\displaystyle \mu_{2}\left(\mu_{2}>\mu_{1}\right)$. Use Huygen's construction of secondary wavelets to trace the retracted wave-front. Hence verify Snell's law of refraction.
Marking-scheme solution
(a)
Tracing the refractive wavefront Verification of Snell's Law of refraction
AB is incident wavefront, incident at an angle i . let \(\displaystyle \tau\) be the time taken by wavefront to travel distance BC .
\(\displaystyle B C=\mathrm{v}_{1} \tau\) where \(\displaystyle \mathrm{v}_{1}\) is speed of wave in medium $\displaystyle 1$
To determine shape of refracted wavefront, we draw a sphere of radius \(\displaystyle \mathrm{v}_{2} \tau\), where \(\displaystyle \mathrm{v}_{2}\) is speed of wave in medium 2.
CE represents a tangent drawn from point C on sphere, CE is the refracted wavefront.
\(\displaystyle \sin i=\frac{B C}{A C}=\frac{\mathrm{v}_{1} \tau}{A C}\) and
\(\displaystyle \sin r=\frac{A E}{A C}=\frac{\mathrm{v}_{2} \tau}{A C}\)
Where i and r are the angles of incidence and refraction, respectively.
\[\frac{\sin i}{\sin r}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\frac{\mu_{2}}{\mu_{1}}
\]
\(\displaystyle \mu_{1} \sin i=\mu_{2} \sin r\)
This is the Snell's law of refraction.
OR
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