A vessel of depth is half filled with oil of refractive index and the other half is filled with water of refractive index . The apparent depth of this vessel when viewed from above will be [2023]

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Q.
A vessel of depth $' d'$ is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$ . The apparent depth of this vessel when viewed from above will be [2023]

Solution

Q.
A vessel of depth $' d'$ is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$ . The apparent depth of this vessel when viewed from above will be [2023]

1 $\frac{d n_{1} n_{2}}{(n_{1} + n_{2})}$

2 $\frac{d (n_{1} + n_{2})}{2 n_{1} n_{2}}$

3 $\frac{d n_{1} n_{2}}{2 (n_{1} + n_{2})}$

4 $\frac{2 d (n_{1} + n_{2})}{n_{1} n_{2}}$

Ans.
(2)

Formula used $d_{app} = \frac{d_{1}}{n_{1}} + \frac{d_{2}}{n_{2}}$

$d_{app} = \frac{d}{2} [\frac{n_{1} + n_{2}}{n_{1} n_{2}}]$

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Solution

Q. 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 [2023]

1 dn1n2(n1+n2)

2 d(n1+n2)2n1n2

3 d n1n22(n1+n2)

4 2d(n1+n2)n1n2

Ans. (2) Formula used dapp=d1n1+d2n2 dapp=d2[n1+n2n1n2]

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Q.
A vessel of depth $' d'$ is half filled with oil of refractive index $n_{1}$ and the other half is filled with water of refractive index $n_{2}$ . The apparent depth of this vessel when viewed from above will be [2023]

1 $\frac{d n_{1} n_{2}}{(n_{1} + n_{2})}$

2 $\frac{d (n_{1} + n_{2})}{2 n_{1} n_{2}}$

3 $\frac{d n_{1} n_{2}}{2 (n_{1} + n_{2})}$

4 $\frac{2 d (n_{1} + n_{2})}{n_{1} n_{2}}$

Ans.
(2)

Formula used $d_{app} = \frac{d_{1}}{n_{1}} + \frac{d_{2}}{n_{2}}$

$d_{app} = \frac{d}{2} [\frac{n_{1} + n_{2}}{n_{1} n_{2}}]$