Question

If a solid transparent object has an refractive index of $2.90$ and a clear liquid has a refractive index of $1.45$ then, which of the following must be true for total internal reflection to occur at the interface between these two media?

• A. Incident beam originates in the solid at an angle of incidence greater than ${30}^o$
• B. Incident beam originates in the liquid at an angle of incidence greater than ${30}^o$
• C. Incident beam originates in the solid at an angle of incidence greater than ${60}^o$
• D. Incident beam originates in the liquid at an angle of incidence greater than ${60}^o$
• E. Total internal reflection cannot occur

Answer 1

The correct option is A Incident beam originates in the solid at an angle of incidence greater than ${30}^o$

There are two necessary conditions for total internal reflection

(i) The light beam must go from denser to rarer medium.

(ii) Angle of incidence must be greater than critical angle.

here solid medium has greater refractive index, therefore, it is a denser medium and beam must go from solid medium to liquid medium i.e. it must originates in solid medium.

now angle of incidence is given by

$\sin C=\frac{{\mu }_{rarer}}{{\mu }_{denser}}=\frac{1.45}{2.90}=0.5000$

or $\sin C=\sin 30$

or $C=30$

therefore angle of incidence must be greater than $30$ degree.