JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Geometrical Optics

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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 ______.

Answer: 158

Solution

The observer's line of sight through the hole makes

4 5^{\circ}

with the vertical, since it runs from the hole to a point

15

cm across and

15

cm down, giving

sin i = \frac{1}{2}

. After the liquid is added to a depth of

30

cm, the refracted ray reaches the far bottom edge,

15

cm across and

30

cm down, so

sin r = \frac{15}{1 5 ^{2} + 3 0 ^{2}} = \frac{1}{5}

. Snell's law gives

n = \frac{s i n i}{s i n r} = \frac{1/ 2}{1/ 5} = \frac{5}{2} = 1.58

, so with

n = \frac{N}{100}

the value is

N = 158

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Integer answer

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JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Geometrical Optics

Solution

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