(C) In the first case,$\theta$ is the critical angle for the glass-air interface. According to the definition of the critical angle,$\sin \theta = \fr

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$\sin^{-1}\left(\frac{1}{\mu^2}\right)$

(C) In the first case,$\theta$ is the critical angle for the glass-air interface. According to the definition of the critical angle,$\sin \theta = \frac{1}{\mu}$. In the second case,light travels from air to glass. Using Snell's law,$\frac{\sin i}{\sin r} = \mu$,where $i = \theta$. Therefore,$\sin r = \frac{\sin \theta}{\mu}$. Substituting $\sin \theta = \frac{1}{\mu}$ into the equation,we get $\sin r = \frac{1/\mu}{\mu} = \frac{1}{\mu^2}$. Thus,the angle of refraction is $r = \sin^{-1}\left(\frac{1}{\mu^2}\right)$.

Class 12 Physics Ray Optics and Optical Instruments Critical Angle and Total Internal Reflection

Medium

$A$ glass slab has a refractive index ' $\mu$ ' with respect to air,and the critical angle for a ray of light going from glass to air is ' $\theta$ '. If a ray of light is incident from air on the glass with an angle of incidence ' $\theta$ ',then the corresponding angle of refraction is:

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A
$\sin^{-1}\left(\frac{1}{\sqrt{\mu}}\right)$
B
$\sin^{-1}\left(\frac{1}{\mu}\right)$
C
$\sin^{-1}\left(\frac{1}{\mu^2}\right)$
D
$90^{\circ}$

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Ray Optics and Optical Instruments

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Critical Angle and Total Internal Reflection

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$A$ glass slab has a refractive index ' $\mu$ ' with respect to air,and the critical angle for a ray of light going from glass to air is ' $\theta$ '. If a ray of light is incident from air on the glass with an angle of incidence ' $\theta$ ',then the corresponding angle of refraction is:

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$A$ rectangular glass block is placed on a printed paper lying on a horizontal surface. Find the minimum refractive index of the glass for which the letters on the paper are not visible from any of the vertical sides of the block.

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$A$ light wave enters from medium $1$ to medium $2$. Its velocity in the $2^{nd}$ medium is double that in the $1^{st}$ medium. For total internal reflection,the angle of incidence must be greater than.......$^o$.

The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air,the angle of incidence,at which it will be totally internally reflected,is ......... $^o$

$A$ small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \; m$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x \,\pi \; m^{2}$. The value of $x$ is ...............

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