MCQ
A beaker containing liquid is placed on a table, underneath a microscope which can be moved along a vertical scale. The microscope is focussed, through the liquid onto a mark on the table when the reading on the scale is $a$. It is next focussed on the upper surface of the liquid and the reading is $b$. More liquid is added and the observations are repeated, the corresponding readings are $c$ and $d$. The refractive index of the liquid is
  • $\frac{d-b}{d-c-b+a}$
  • B
    $\frac{b-d}{d-c-b+a}$
  • C
    $\frac{d-c-b+a}{d-b}$
  • D
    $\frac{d-b}{a+b-c-d}$

Answer

Correct option: A.
$\frac{d-b}{d-c-b+a}$
The real depth $=\mu$ ( apparent depth)$\Rightarrow$ In first case, the real depth $h_1=\mu(b-a)$
Similarly in the second case, the real depth $h_2=\mu(d-c)$Since $h_2>h_1$, the difference of real depths $=h_2-h_1=\mu(d-c-b+a)$
Since the liquid is added in second case, $h_2-h_1=(d-b)$$\Rightarrow \mu=\frac{(d-b)}{(d-c-b+a)}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A big ball of mass $M$, moving with velocity $u$ strikes a small ball of mass $m$, which is at rest. Finally small ball obtains velocity $u$ and big ball $v$. Then what is the value of $v$
The atmosphere is held to the earth by
A man can see the object between $15 \mathrm{~cm}$ and $30 \mathrm{~cm}$. He uses the lens to see the far objects. Then due to the lens used, the near point will be at
Two identical cylindrical vessels with their bases at same level each contains a liquid of density $\rho$. The height of the liquid in one vessel is $h_1$ and that in the other vessel is $h_2$. The area of either base is$A$. The work done by gravity in equalizing the levels when the two vessels are connected, is
The force $F$ on a sphere of radius ' $a$ ' moving in a medium with velocity ' $v$ ' is given by $F=6 \pi \eta a v$. The dimensions of $\eta$ are
A uniform magnetic field of $3000\,G$ is established in the positive $z-$ direction. A rectangular loop of side $10\,cm$ and $5\,cm$ carries a current of $12\,A.$ What is the magnitude of placed as shown torque on the loop is
The potential energy of a particle executing S.H.M. is 2.5 J, when its displacement is half of amplitude. The total energy of the particle be
In Young's double slit experiment, if monochromatic light is replaced by white light

Image

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude $a$ is
An alternating current of frequency $200 \mathrm{rad} / \mathrm{sec}$ and peak value $1 A$ as shown in the figure, is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is $1.5 \mathrm{H}$, the voltage induced in the secondary will be
Image