Apparent depth of $X$ in all three cases are $H_{1} H_{2}, H_{3}$ respectively when seen from aboove, then
(given $H = 30 c m, n = 1.5$ and $R = 3 m$

0.8 < H_{2} - H_{1} < 0.9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

H_{2} > H_{1}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

H_{2} > H_{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

H_{3} > H_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $H_{2} > H_{3}$
Case 1: When the surface is flat then the surface will behave like a glass slab

$H_{1} = \frac{H}{η} = \frac{30 \times 2}{3} = 20 c m$

Case 2:
Now, we will apply the formula for refraction on curved surface
$\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}$
$\frac{1}{- H_{2}} - \frac{1.5}{- 30} = \frac{1 - 1.5}{- 300}$
$H_{2} = 20.68 c m$

Case 3:

Again we will apply the formula for refraction on curved surface
$\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}$
$\frac{1}{- H_{3}} - \frac{1.5}{- 30} = \frac{1 - 1.5}{300}$
$H_{3} = \frac{600}{31} = 19.35 c m$
Conclusion:
$H_{2} > H_{1} > H_{3}$
$H_{2} - H_{1} = 20.68 - 20 = 0.68$

Suggest Corrections

Similar questions

There are three setups, shown in figure. Voltage of ends are given, heat developed in 1, 2 and 3 are

H_{1}, H_{2}

and

H_{3}

, then

Three glass cylinders of equal height $H = 30 c m$ 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

Q. If a

△ A B C

has altitudes

h_{1}, h_{2}, h_{3}

and inradius

r

, then the minimum value of

\frac{h_{1} + r}{h_{1} - r} + \frac{h_{2} + r}{h_{2} - r} + \frac{h_{3} + r}{h_{3} - r}

A stone falls freely under gravity, covers distance $h_{1}, h_{2}$ and $h_{3}$ in the first 5 sec, the next 5 sec and the further next 5 sec respectively. The relation between $h_{1}, h_{2}$ and $h_{3}$ is: