devarshi-dt-logo

Question:

Three glass cylinders of equal height H=30cm and same refractive index n=1.5 are placed on a horizontal surface as 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: A) 0.8cm < (H2−H1) < 0.9cm B) H3 > H1 C) H2 > H1 D) H2 > H3

0.8cm<(H2−H1)<0.9cm

H3>H1

H2>H1

H2>H3

Solution:

Correct option is D. H2 > H3
Case - I
H=30cm
n=3/2
H1=H/n ⇒ 30 × 2/3 = 20cm
Case - II
R=300cm
n2v − n1u = (n2 − n1)/R
1/H2 − 3/(-2) × 30 = (1 − 3)/2 (−300)
H2 = 600/29 = 20.684cm
Case - III :
n2v − n1u = (n2 − n1)/R ; 1/H3 − 3/(-2) × 30 = (1 − 3)/2 (300) ; H3 = 600/31 = 19.354cm