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Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments5 Marks
Question
When a light ray passes from the atmosphere (a) through the combination of two mediums water (b) and glass (c), then find the relationship between the refractive indices of the three mediums.
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Answer

Applying Snell's law on points A, B and C, we obtained :
$n_{21}=\frac{\sin i}{\sin r_1}\ldots(i)$
$n_{32}=\frac{\sin r_1}{\sin r_2}\ldots(ii)$
and $\quad$ $n_{31}=\frac{\sin r_2}{\sin i} \ldots(iii)$
Image

Multiplying (i), (ii) and (iii) :
$
n_{21} \times n_{32} \times n_{31}=\frac{\sin i}{\sin r_1} \times \frac{\sin r_1}{\sin r_2} \times \frac{\sin r_2}{\sin i}=1
$
or $\quad$ $n_{21} \times n_{32}=\frac{1}{n_{31}}=n_{31}$
or $\quad$ $\underline {n_{32}=\frac{n_{31}}{n_{21}}}$

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