Ray Optics

JEE Main level, single correct, medium

87 of 295

Question 87 of 295

A vessel of depth dd is half filled with oil of refractive index n1{n}_{1} and the other half is filled with water of refractive index n2.{n}_{2}. The apparent depth of this vessel when viewed from above will be-

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Answer: (B) d(n1+n2)2n1n2\dfrac{d\left({n}_{1}+{n}_{2}\right)}{2{n}_{1}{n}_{2}}

The apparent depth formula is given by n=RealdepthApparentdepthn=\dfrac{Realdepth}{Apparentdepth}.
The apparent depth in this case is given by
d′=d1n1+d2n2⇒d′=d2(1n1+1n2)⇒d′=d2(n1+n2n1n2)d'=\dfrac{{d}_{1}}{{n}_{1}}+\dfrac{{d}_{2}}{{n}_{2}} \Rightarrow d'=\dfrac{d}{2}(\dfrac{1}{{n}_{1}}+\dfrac{1}{{n}_{2}}) \Rightarrow d'=\dfrac{d}{2}(\dfrac{{n}_{1}+{n}_{2}}{{n}_{1}{n}_{2}})

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