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  4. A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is

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Q. A point source $S$ is placed at the bottom of a transparent block of height $10\, mm$ and refractive index $2.72$. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter $11.54\, mm$ on the top of the block. The refractive index of the liquid isPhysics Question Image

JEE AdvancedJEE Advanced 2014Ray Optics and Optical Instruments

Solution:

image
rays from the point source can be seen from outside only if they refract at the surface and can come out, this happens only till angle of incidence of light ray from source is below critical angle . and at critical angle it graces by Snell's law .
$2.72 \sin \alpha=\mu \times \sin 90^{\circ}$
$
\frac{2.72 \times 5.77}{11.54}=\mu
$
$
\mu=1.36
$
refractive index of outer region is $1.36$