A student sees the top edge and the bottom centre C of a pool sim… - Vidyadip

Question

A student sees the top edge and the bottom centre $C$ of a pool simultaneously from an angle $\theta$ above the horizontal as shown in the figure. The refractive index of water which fills up to the top edge of the pool is $\frac{4}{3} .$ If $\frac{h}{x}=\frac{7}{4}$, then $\cos \theta$ is

✓

Answer

(c)

Ray diagram for pool is as shown below.

Using $n_1 \cdot \sin i=n_2 \cdot \sin r$, we have

$1 \times \sin \left(90^{\circ}-\theta\right)=\frac{4}{3} \sin r \quad \dots(i)$

$\text { Also, } \tan r=\frac{x}{2 h}=\frac{4}{7 \times 2}=\frac{2}{7}$

$\Rightarrow \sin r=\frac{2}{\sqrt{53}} \overline{ }$

Substituting $\sin r$ in Eq. $(i)$, we have

$\cos \theta=\frac{4}{3} \times \frac{2}{\sqrt{5} \overline{3}}=\frac{8}{3 \sqrt{53}}$

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 linear momentum $p$ of a body of mass $5 \,kg$ varies with time $t$ as, $p = 5t^2 + t + 5$ It follows that the body is moving with

Assertion : Neutrons penetrate mater more readily as compared to protons.

Reason : Neutrons are slightly more massive than protons.

For what value of the resistor $X$ will the equivalent resistance of the two circuits shown be the same?

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

The potential energy of a weight less spring compressed by a distance $ a $ is proportional to

An iron rod of length $2m$ and cross section area of $50\,m{m^2}$, stretched by $0.5\, mm$, when a mass of $250\, kg$ is hung from its lower end. Young's modulus of the iron rod is

A spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be

Two isolated metallic spheres of radii $2 \,cm$ and $4 \,cm$ are given equal charge, then the ratio of charge density on the surfaces of the spheres will be

A transistor is operating in the active mode. $v_1$ is potential barrier across base emitter junction and $v_2$ is potential barrier across collector base junction. $b_1$ is width of depletion layer of base emitter junction and $b_2$ is width of collector base junction.

An electron of stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired a result of photon emission will be