The speed of light in media $A$ and $B$ are $2.0 \times 10^{10} \, cm/s$ and $1.5 \times 10^{10} \, cm/s$ respectively. $A$ ray of light enters from medium $B$ to $A$ at an incident angle $\theta$. If the ray suffers total internal reflection,then:

  • A
    $\theta = \sin^{-1}\left(\frac{3}{4}\right)$
  • B
    $\theta > \sin^{-1}\left(\frac{2}{3}\right)$
  • C
    $\theta < \sin^{-1}\left(\frac{3}{4}\right)$
  • D
    $\theta > \sin^{-1}\left(\frac{3}{4}\right)$

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$A$ planar structure of length $L$ and width $W$ is made of two different optical media of refractive indices $n_1=1.5$ and $n_2=1.44$ as shown in the figure. If $L \gg W$,a ray entering from end $AB$ will emerge from end $CD$ only if the total internal reflection condition is met inside the structure. For $L = 9.6 \ m$,if the incident angle $\theta$ is varied,the maximum time taken by a ray to exit the plane $CD$ is $t \times 10^{-9} \ s$,where $t$ is. . . . . . . [Speed of light $c = 3 \times 10^8 \ m/s$]

Material $A$ has a critical angle ${i_A},$ and material $B$ has a critical angle ${i_B}$ $({i_B} > {i_A})$. Then which of the following is true?
$(i)$ Light can be totally internally reflected when it passes from $B$ to $A$.
$(ii)$ Light can be totally internally reflected when it passes from $A$ to $B$.
$(iii)$ The critical angle for total internal reflection is ${i_B} - {i_A}$.
$(iv)$ The critical angle between $A$ and $B$ is ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.

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What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding,respectively?

$A$ point source of light is placed at a depth $h = 0.5 \, m$ below the surface of a liquid $(\mu = \frac{5}{4})$. Then,the fraction of light energy that escapes directly from the liquid surface is:

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