A vessel is half filled with a liquid of refractive index m. The other half of the vessel is filled with an immiscible liquid of refrative index 1.5 μ. The apparent depth of the vessel is 50% of the actual depth. Then μ is(a) 1.4(b) 1.5(c) 1.6(d) 1.67
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Secondary SchoolMath 13 points
A vessel is half filled woth a liquid of refractive index n. the other half
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chenu1011
chenu1011 Ambitious
I presume that the answer is 1.67.
I applied the formula apparent depth= d/2 ( 1/n1+ 1/n2 )
where d is the real depth and n1 and n2 are the refractive indices
OR
Expression for refractive index:
μ=Real depthApparent depth
Half filled with refractive index n:
Apparent depth =Real depthn
=d/2n
=d2n
Other half filled with refractive index 1.5n:
Apparent depth =Real depth1.5n
=d/21.5n=d3n
Total apparent depth:
Total apparent depth=d2n+d3n =5d6n
But, total apparent depth is d/2.
Hence,
5d6n=d26n=10 n=106 =1.67
HOPE IT HELP YOU.