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Asked by arpitarout132 | 30 Apr, 2022, 16:38: PM
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Before partially filling the tank with liquid , if convex lens forms image at 30 cm above lens for the object
at a distance 60 cm below lens, then the focal length of convex lens is detrmined from the lens equation .
 
(1/v) - (1/u) = (1 / f )
 
where v = 30 cm is lens-to-image distance and u = -60 cm is lens-to-object distance
 
( Cartesian sign convention is followed )
 
Hence lens equation becomes , ( 1 / f ) = ( 1/30 ) + (1/ 60) = 1/20 
 
focal length of convex lens f = 20 cm.
 
After filling the tank with liquid of unknown refractive index upto a depth 40 cm , if image is shifted by 15 cm ,
then apparent object distance is calculated using lens equation by considering lens-to-image distance as v = 45 cm
 
(1/45) -(1/u) = 1/20  or (1/u) = (1/45) - (1/20) = - 1/36  or   u = -36 cm
 
Hence Apparent depth = (60-36 ) = 24 cm
 
refractive index = Real depth / Apparent depth = 40 / 24 = 1.667
Answered by Thiyagarajan K | 30 Apr, 2022, 22:25: PM
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