Let the x-z plane be the boundary between two transparent media. Medium 1 in z\geq 0 has a refractive index of \sqrt{2} and medium 2 with z< 0 has a refractive index of \sqrt{3}. . A ray of light in medium 1 given by the vector \vec{A}= 6\sqrt{3}\: \hat{i}+8\sqrt{3}\: \hat{j}-10\: \hat{k} is incident on the plane of separation. The angle of refraction in medium 2 is

  • Option 1)

    30^{\circ}

  • Option 2)

    45^{\circ}

  • Option 3)

    60^{\circ}

  • Option 4)

    75^{\circ}

 

Answers (1)

As we learnt in

Relation between angle of incidence and angle of refaction -

\mu _{1}\sin i= \mu _{2}\sin r
 

- wherein

\mu _{1}= refractive index of medium of incidence.

\mu _{2}=  refractive index of medium where rays is refracted.

i= angle of incidence.

r= angle of refraction.

 

 \vec{A}=6\sqrt{3}\ \widehat{i}+8\sqrt{3}\ \widehat{j}-10\widehat{k}

cos \widehat{i}=\frac{10}{(6\sqrt{3})^{2}+(8\sqrt{3})^{2}+(-10)^{2}}=\frac{10}{20}

cos i=\frac{1}{2}=i=cos^{-1}(1/2)

i=60^{o}

From Snell's law

\mu_{1}sini=\mu_{2}sinr

\sqrt{2}sin60^{o}=\sqrt{3}sinr

\Rightarrow\ \; r = 45^{o}

Correct option is 2.

 


Option 1)

30^{\circ}

This is an incorrect option.

Option 2)

45^{\circ}

This is the correct option.

Option 3)

60^{\circ}

This is an incorrect option.

Option 4)

75^{\circ}

This is an incorrect option.

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