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A ray of light travelling in a transpatent medium of refractive index \mu, falls on a surface separating the medium from air at an angle of incidence of 45^{\circ}. For which of the following value of \mu the ray can undergo total internal reflection?

  • Option 1)

    \mu =1.33

  • Option 2)

    \mu=1.40

  • Option 3)

    \mu =1.50

  • Option 4)

    \mu =1.25

 

Answers (1)

best_answer

 

Critical angle -

sin c = Refractive index of rarer medium / Refractive index of denser medium

- wherein

When angle of incidence of a travelling from a dence medium to rarer medium is greater than critical angle, no refraction occurs.

 

 For total internal reflection \theta \geq \theta _{c}

Sin \theta_{c}=\frac{1}{\mu} => \theta_{c}=sin^{-1}(\frac{1}{\mu})

\theta\geq sin^{-1}(\frac{1}{\mu}) or Sin\theta\geq \frac{1}{\mu} or \mu\geq \frac{1}{sin\theta}

\mu\geq \frac{1}{Sin 45}\mu\geq \frac{1}{Sin 45} =\sqrt{2}

Only value satisfy this is \mu=1.50

 


Option 1)

\mu =1.33

This is incorrect answer 

Option 2)

\mu=1.40

This is correct answer 

Option 3)

\mu =1.50

This is incorrect answer 

Option 4)

\mu =1.25

This is incorrect answer 

Posted by

divya.saini

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