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  • A vessel of depth 'd' is half filled with oil of refractive index n1 and the other half is filled with water of refractive index n2. The apparent depth of this vessel when viewed fro

A vessel of depth 'd' is half filled with oil of refractive index n1 and the other half is filled with water of refractive
index n2. The apparent depth of this vessel when viewed from above will be -

 

Option: 1

\frac{\mathrm{d}\left(\mathrm{n}_1+\mathrm{n}_2\right)}{2 \mathrm{n}_1 \mathrm{n}_2}


Option: 2

\frac{\mathrm{d}\left(\mathrm{n}_1+\mathrm{n}_2\right)}{2 \mathrm{n}_1 \mathrm{n}_2}


Option: 3

\frac{\mathrm{dn}_1 \mathrm{n}_2}{2\left(\mathrm{n}_1+\mathrm{n}_2\right)}


Option: 4

\frac{2 \mathrm{~d}\left(\mathrm{n}_1+\mathrm{n}_2\right)}{\mathrm{n}_1 \mathrm{n}_2}


Answers (1)

best_answer

\begin{aligned} & \left(\mathrm{d}_{\text {app }}\right)_1=\frac{\mathrm{d}}{2\left(\frac{\mathrm{n}_1}{\mathrm{n}_2}\right)}=\frac{\mathrm{n}_2 \mathrm{~d}}{2 \mathrm{n}_1} \\ & \left(\mathrm{~d}_{\text {app }}\right)_2=\frac{\left(\mathrm{d}_{\text {app }}\right)_1+\frac{\mathrm{d}}{2}}{\mathrm{n}_2} \\ & =\frac{\left(\frac{\mathrm{n}_2}{\mathrm{n}_1}+1\right) \frac{\mathrm{d}}{2}}{\mathrm{n}_2} \\ & \left(\mathrm{~d}_{\text {app }}\right)_2=\frac{\left(\mathrm{n}_1+\mathrm{n}_2\right) \mathrm{d}}{2 \mathrm{n}_1 \mathrm{n}_2} \end{aligned}

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