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Three glass cylinders of equal height H=30 cm and same refractive index n=1.5...

Three glass cylinders of equal height H=30 cm and same refractive index n=1.5 are placed on a horizontal surface shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same R=3m. If H1,H2 and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are

H3>H1
0.8cm<H2-H1<0.9cm
H2>H3
H2>H1
Solution:

Case- I:

Given, H=30 cm
n=32
Apparent depth H1=H/n30×23=20 cm
Case- II:

R=300 cm
n2v-n1u=n2-n1R (Refraction through curved surface)
1-H2-3-2×30=1-32-300
H2=60029=20.684 cm
Case- III:

n2v-n1u=n2-n1R;1-H3-3-2×30=1-32300;H3=60031=19.354 cm