An air bubble in a glass slab with refractive | vedclass

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(A) Let the thickness of the glass slab be $t$.Let the air bubble be at a distance $x$ from one surface. Then its distance from the opposite surface i

Vedclass · Accepted Answer

$12$

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(A) Let the thickness of the glass slab be $t$.Let the air bubble be at a distance $x$ from one surface. Then its distance from the opposite surface is $(t - x)$.Given the refractive index of the glass slab is $\mu = 1.5$.The apparent depth of the bubble from the first surface is $d_1 = \frac{x}{\mu} = 5\, cm$.So,$x = 5 	imes 1.5 = 7.5\, cm$.The apparent depth of the bubble from the second surface is $d_2 = \frac{t - x}{\mu} = 3\, cm$.So,$t - x = 3 	imes 1.5 = 4.5\, cm$.Adding the two equations: $x + (t - x) = 7.5 + 4.5$.$t = 12\, cm$.Alternatively,the sum of apparent depths is $\frac{x}{\mu} + \frac{t - x}{\mu} = \frac{t}{\mu} = 5 + 3 = 8$.Therefore,$t = 8 	imes 1.5 = 12\, cm$.

An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\, cm$ deep when viewed from one surface and $3\, cm$ deep when viewed from the opposite face. The thickness (in $cm$) of the slab is

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