SATHEE: Optics 2 Question 10

Optics 2 Question 10

10. An observer can see through a pin-hole the top end of a thin rod of height $h$ , placed as shown in the figure. The beaker height is $3 h$ and its radius $h$ . When the beaker is filled with a liquid up to a height $2 h$ , he can see the lower end of the rod. Then the refractive index of the liquid is

(2002, 2M)

(a) $\frac{5}{2}$

(b) $\sqrt{\frac{5}{2}}$

(c) $\sqrt{\frac{3}{2}}$

(d) $\frac{3}{2}$

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Answer:

Correct Answer: 10. (b)

Solution:

$\begin{aligned} P Q = Q R = 2 h \Rightarrow ∠ i = 45^{\circ} \\ ∴ S T = R T = h = K M = M N \\ So, K S = \sqrt{h^{2} + (2 h)^{2}} = h \sqrt{5} \\ ∴ \sin r = \frac{h}{h \sqrt{5}} = \frac{1}{\sqrt{5}} \end{aligned}$

$∴ μ = \frac{\sin i}{\sin r} = \frac{\sin 45^{\circ}}{1 / \sqrt{5}} = \sqrt{\frac{5}{2}}$

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Optics 2 Question 10

10. An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

Answer:

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