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Physics-

General

Easy

Question

In the adjoining diagram, a wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normals drawn at A and D. The refractive index of glass with respect to air ( $mu equals 1$ ) will be equal to

$\frac{\sin θ}{\sin θ}$ '/>
$\frac{\sin θ}{\sin φ}$ '/>
$\sin φ$ sin⁡θ'/>
$\frac{A B}{C D}$

The correct answer is: $fraction numerator sin invisible function application theta over denominator sin invisible function application phi ´ end fraction$

In the case of refraction if CD is the refracted wave front and v₁ and v₂ are the speed of light in the two media, then in the time the wavelets from B reaches C, the wavelet from A will reach D, such that

$t equals fraction numerator B C over denominator v subscript a end subscript end fraction equals fraction numerator A D over denominator v subscript g end subscript end fraction rightwards double arrow fraction numerator B C over denominator A D end fraction equals fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction$ .....(i)
But in $capital delta A C B comma$ $B C equals A C sin invisible function application theta$ .....(ii)
while in $capital delta A C D comma$ $A D equals A C sin invisible function application phi to the power of ´ end exponent$ .....(iii)
From equations (i), (ii) and (iii) $fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction$
Also $mu proportional to fraction numerator 1 over denominator v end fraction rightwards double arrow fraction numerator v subscript a end subscript over denominator v subscript g end subscript end fraction equals fraction numerator mu subscript g end subscript over denominator mu subscript a end subscript end fraction equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction rightwards double arrow mu subscript g end subscript equals fraction numerator sin invisible function application theta over denominator sin invisible function application phi to the power of ´ end exponent end fraction$

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