A large glass slab (μ=(5)/(3)) of thickness 8 cm is placed over a...

A large glass slab

\left(\mu=\frac{5}{3}\right)

of thickness 8

\mathrm{cm}

is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius

R \mathrm{~cm}

. What is the value of

R

Correct answer

Step-by-step solution

\frac{R}{t}=

\tan \theta_C or

\quad R=t\left(\tan \theta_C\right)

\begin{aligned} &\text{ But, }\quad \sin \theta_C=\frac{1}{\mu}=\frac{3}{5} \\ & \therefore \quad \tan \theta_C=\frac{3}{4} \\ & \therefore \quad R=\frac{3}{4} t=\frac{3}{4}(8 \mathrm{ cm})=6 \mathrm{ cm} \\ & \end{aligned}

$$ Hence the answer is 6 .

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