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Q.

In a thick glass slab of thickness $l$ , and refractive index n₁ a cuboidal cavity of thickness 'm' is carved as shown in figure and is filled with a liquid of RI n₂ (n₁ > n₂). The ratio $l$ /m, so that shift produced by this slab is zero when an observer r4 observes
an object B with paraxial rays is

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a

$\frac{n_{1} - n_{2}}{n_{2} (n_{1} - 1)}$

b

$\frac{n_{1} - n_{2}}{n_{1} - 1}$

c

$\frac{n_{1} - n_{2}}{n_{2} - 1}$

d

$\frac{n_{1} - n_{2}}{n_{1} (n_{2} - 1)}$

answer is B.

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Detailed Solution

$Shift = (l - m) (1 - \frac{1}{n_{1}}) + m (1 - \frac{1}{n_{2}}) = 0$

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In a thick glass slab of thickness l, and refractive index n1 a cuboidal cavity of thickness 'm' is carved as shown in figure and is filled with a liquid of RI n2 (n1 > n2). The ratio l/m, so that shift produced by this slab is zero when an observer r4 observesan object B with paraxial rays is