Question 368: 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 H
1
, 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
![](https://imagex.cdn.examgoal.net/1kszbi4o0/2fce7ae1-d17b-4d03-86cd-6720dbecb8e1/4e3f1200-09f0-11ec-a8f3-9320288f0d0d/file-1kszbi4o1.jpeg)

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
![](['https://imagex.cdn.examgoal.net/1kszbptz3/40b0808e-afd0-4529-aa86-3cbde936dd9e/2475c8f0-09f1-11ec-b419-f733eb33510a/file-1kszbptz4.jpeg', 'https://imagex.cdn.examgoal.net/1kszbrtec/cea0b088-6a2d-4f74-9517-ce0326e47e0f/5ba21540-09f1-11ec-b419-f733eb33510a/file-1kszbrted.jpeg', 'https://imagex.cdn.examgoal.net/1kszbt8cy/8883f3b2-b405-4f53-afa9-3c70e3c2d873/82ffe720-09f1-11ec-b419-f733eb33510a/file-1kszbt8cz.jpeg'])

Answer

H
2
> H
1

Answer

H
3
> H
1

Answer

0.85 cm < (H
2
$ - $ H
1
) < 0.9 cm

Answer

H
2
> H
3

Ray Optics

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