A) How fast is the light travelling in the liquid? \[1.8\times {{10}^{8}}\,m/s\]
B) \[2.4\times {{10}^{8}}\]
C) \[3.0\times {{10}^{8}}\,m/s\]
D) \[1.2\times {{10}^{8}}\,m/s\]
Correct Answer: A
Solution :
Key Idea: Critical angle is the angle of incidence in denser medium for which the angle of refraction in rarer medium is \[{{90}^{\text{o}}}\]. As shown in figure, a light ray from the coin will not emerge out of liquid, if \[i>C\]. Therefore, minimum radius R corresponds to i = C. In \[\Delta \,\,SAB,\] \[\frac{R}{h}=\tan C\] or R = h tan C \[orR=\frac{h}{\sqrt{{{\mu }^{2}}-1}}\] Given, R = 3 cm, h = 4 cm Hence, \[\frac{3}{4}=\frac{1}{\sqrt{{{\mu }^{2}}-1}}\] or \[{{\mu }^{2}}=\frac{25}{9}\,or\,\mu =\frac{5}{3}\] But \[\mu =\frac{c}{v}or\,v=\frac{c}{\mu }\] \[=\frac{3\times {{10}^{8}}}{5/3}\] \[=1.8\times {{10}^{8}}\,m/s\]You need to login to perform this action.
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