Question 18: Ray Optics

Question

Three glass cylinders of equal height H = 30 cm 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 = 3 m). 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

Accepted Answer

Case - I
H = 30 cm
n = $${3 \over 2}$$
H
1
= $${H \over n}$$
$$ \Rightarrow $$ $${{30 	imes 2} \over 3}$$ = 20 cm
Case - II
R = 300 cm
$${{{n_2}} \over v} - {{{n_1}} \over u} = {{{n_2} - {n_1}} \over R}$$
$${1 \over { - {H_2}}} - {3 \over { - 2 	imes 30}} = {{1 - {3 \over 2}} \over { - 300}}$$
$${H_2} = {{600} \over {29}} = 20.684$$ cm
Case - III
$${{{n_2}} \over v} - {{{n_1}} \over u} = {{{n_2} - {n_1}} \over R}$$;
$${1 \over { - {H_3}}} - {3 \over { - 2 	imes 30}} = {{1 - {3 \over 2}} \over {300}}$$
$${H_3} = {{600} \over {31}} = 19.354$$ cm

Answer

H2 > H1

Answer

H3 > H1

Answer

0.85 cm < (H2 $$ - $$ H1) < 0.9 cm

Answer

H2 > H3

Ray Optics

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