A large square container with thin transparent vertical walls and… - Vidyadip

Question

A large square container with thin transparent vertical walls and filled with water (refractive index $\frac{4}{3}$ ) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water $12 cm$ from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in $cm$ ) between these images is . . . . .

✓

Answer

We will assume that observer sees the image of object through edge $\Rightarrow \alpha=45^{\circ}$

$AB =\frac{12 d \alpha}{\cos \alpha}=\frac{ xd \theta}{\cos \theta}$

By applying Snell's Law

$\frac{4}{3} \sin \alpha=1 \sin \theta$

$\frac{4}{3} \cos \alpha d \alpha=\cos \theta d \theta$

$\Rightarrow \frac{9}{\cos ^2 \alpha}=\frac{x}{\cos ^2 \theta}$

$1 \sin \theta=\frac{4}{3} \sin \alpha$

$\Rightarrow \sin \theta=\frac{2 \sqrt{2}}{3} \Rightarrow x=18 \times \frac{1}{9}=2$

$d=2 x \sin (\theta-\alpha)$

$=4 \times \frac{1}{\sqrt{2}}\left(\frac{2 \sqrt{2}}{3}-\frac{1}{3}\right)=\frac{8-2 \sqrt{2}}{3} \approx 1.73 \approx 2$

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

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The potential difference $(V_A - V_B)$ between the points $A$ and $B$ in the given figure is ............ $V$

A wire having mass $m$ and length $1$ can freely slide on a pair or parallel smooth horizontal rails placed in vertical magnetic field $B$. The rails are connected by a capacitor of capacitance $C$. The electric resistance of the rails and the wire is zero. If a constant force $F$ acts on the wire as shown in the figure. Then, the acceleration of the wire can be given as

The stopping potential doubles when the frequency of the incident light changes from $v$ to $\frac{3v}{2}$ . Then the work function of the metal must be

If the charge on a capacitor is increased by $2$ coulomb, the energy stored in it increases by $21\%$. The original charge on the capacitor is....$C$

This is the position time graph of a mass on spring. What can you say about the velocity and force at the instant indicated by dashed line ? (positive direction is to the right)

The ratio of lengths of two rods $A$ and $B$ of same material is $1 : 2$ and the ratio of their radii is $2 : 1$, then the ratio of modulus of rigidity of $A$ and $B$ will be

When heat is given to a gas in an isothermal change, the result will be

A body with mass $2\, kg$ moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at $x = 2m$, then its speed when it crosses $x = 5\, m$ is ................ $\mathrm{m}/ \mathrm{s}$

If the angles of dip at two places are $30^o$ and $45^o$ respectively, then the ratio of horizontal components of earth's magnetic field at the two places will be

An optical fibre consists of core of $\mu_1$ surrounded by a cladding of $\mu_2$ < $\mu_1$. A beam of light enters from air at an angle $\alpha$ with axis of fibre. The highest $\alpha$ for which ray can be travelled through fibre is