Question 330: Ray Optics

Question

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of
15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a
liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the
refractive index of the liquid is N/100, where N is an integer, the value of N is _____.

Accepted Answer

tan r = $${{15} \over {30}}$$ = $${1 \over 2}$$
sin r = $${1 \over {\sqrt 5 }}$$
1sin 45
o
= $$\mu $$sin r
$$ \Rightarrow $$ $${1 \over {\sqrt 2 }} = \mu \left( {{1 \over {\sqrt 5 }}} \right)$$
$$ \Rightarrow $$ $$\mu $$ = $$\sqrt {{5 \over 2}} $$ = 1.58
$$\mu  = {N \over {100}}$$ = 1.58
$$ \Rightarrow $$ N = 158

Ray Optics

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