Question

A glass slab 2.5 cm thick is placed over a coin. If the refractive index of glass is
3/2, find the height through which the coin is raised​

Answer 1

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Height by which it is raised = It's apparent depth = 5/3cm.

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Refractive index of a medium is the ratio of speed of light in air to speed of light in that medium. Refractive index has no unit. It is represented by :

$r.i \: = \frac{velocity \: of \: light \: in \: air}{velocity \: of \: light \: in \: given \: medium}$

Refractive index is also represented by two more equations they are :

$r.i \: = \frac{sin \: of \: angle \: of \: incidence}{sin \: \: of \: angle \: of \: refraction}$

$r.i \: = \frac{real \: depth}{apparent \: depth}$

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It is given that:-

Refractive index of glass = 3/2

Real depth of coin = 2.5cm

Now according to the third equation used to denote refractive index, we can say

$refractive \: index = \frac{real \: depth}{apparent \: depth}$

After inputting the known values we get :

$\frac{3}{2} = \frac{2.5}{apparent \: depth}$

$apparent \: depth = \frac{2.5 \times 2}{3} = \frac{5}{3}$

Thus the apparent depth of coin is 5/3cm.

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BY SCIVIBHANSHU

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