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Ask iit jee aieee pet cbse icse state board experts Expert Question: apparent depth and normal displacement
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kshitijgunit (0)

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how do you find the total normal displacement if an oblect is placed say beneath a glass slab over which is kept a beaker of water when viewed from air?
i can solve such a numerical by direct application of the derieved formulae but fail to understand it physically...
"My conception":--
(1) a ray travels from the object to the glass water interface normally, and thus undeviated.
(2) an inclined ray travels from the object to the glass - water interface, adn suffers its "first" refraction, which when produced backwards intersects with the undeviated ray to form an img..
(3) the img now acts like a virtual object for the water- air interface, whose refracted ray when produced backwards cuts the undeviated ray to form the final img whose position helps to find the normal displacement..
 
to find the normal disp of the 1st img (say ur eyes are in water), do u use the absolute R.I or the relative R.I of glass w.r.t water???
 
after finding out the disp. due to glass, does the apparent depth due to glass become the real depth for displacement due to water??
 
can it ever be that the 1st image not be in glass but in water??
 
please explain wherevr iv gone wrong..and clear my doubt!!!
 
thnx a million!!
 
 
 
    
neeraj_agarwal_1990 (887)

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we have a general formula for that...

h= n( t1/n1 + t2/n2 +t3/n3+.....)
where n is refractive index of outer medium and n1 ,n2 , n3 ...are refractive index of layers...
t1,t2,t3 ...are thickness...
h is the height of image...
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elessar_iitkgp (2259)

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Good solution Neeraj
Lets derive the steps though.

Consider a beaker having water upto height h, kept over a slab of thickness t.
Let the bootom point surface of the slab be A, the beaker-slab interface be B, and the water-air interface be C.
Then,BA = t
BI1 = t/n1 (Assuming the water to be less dense the slab's material)
CI1 = h + t(nw/ng)
CI2 = (h + t(nw/ng))/nw = h/nw + t/ng

Remember this,
Write the object distance from the refracting surface
To get the image distance,
Divide or multiply by the refractive index, as the image distance decreases or increases.  (if one of the medium is air)
If the boundary is between such that one of the materials isn't air (r.i = 1), the multiply the ratios of r.i's. If the image distance increase, multiply by (r.i of denser/r.i of rarer), otherwise if image distance reduces, multiply by (r.i of rarer/r.i of denser)



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