Three glass cylinders of equal height H = 30 cm and same refractive index 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. [2019]

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 $H_{1}$ , $H_{2}$ and $H_{3}$ are the apparent depths of a point (X) on the bottom of the three cylinders, respectively, the correct statement(s) is/are : [2019]

Smart Achievers · Accepted Answer

(2, 4)

As we know, $μ = \frac{real depth}{apparent depth}$

Case - I $H_{2}$

Case - II $\frac{- n_{1}}{u} + \frac{n_{2}}{v} = \frac{n_{2} - n_{1}}{R}$

$∴$ $\frac{- 1.5}{- 30} + \frac{1}{- H_{2}} = \frac{1 - 1.5}{- 300}$ $∴$ $H_{2} = 20.68 cm$

Case - III $∴$ $\frac{- 1.5}{- 30} + \frac{1}{- H_{3}} = \frac{1 - 1.5}{300}$

$∴$ $\frac{1}{- H_{3}} = - \frac{1}{600} - \frac{1}{20}$

$∴$ $H_{3} = 19.35 cm$

Solution

1 $0.8 cm < (H_{2} = H_{1}) < 0.9 cm$

2 $H_{2} > H_{1}$

3 $H_{3} > H_{1}$

4 $H_{2} > H_{3}$

Want Us to Email you About Special Offers & Updates?

Solution

1 0.8 cm<(H2=H1)<0.9 cm

2 H2>H1

3 H3>H1

4 H2>H3

Ans. (2, 4) As we know, μ=real depthapparent depth Case - I H1=H1.5=301.5=20 cm Case - II -n1u+n2v=n2-n1R ∴ -1.5-30+1-H2=1-1.5-300 ∴ H2=20.68 cm Case - III ∴ -1.5-30+1-H3=1-1.5300 ∴ 1-H3=-1600-120 ∴ H3=19.35 cm

Want Us to Email you About Special Offers & Updates?

1 $0.8 cm < (H_{2} = H_{1}) < 0.9 cm$

2 $H_{2} > H_{1}$

3 $H_{3} > H_{1}$

4 $H_{2} > H_{3}$