A) \[\mu =\frac{3+\sqrt{5}}{2}\]
B) \[\mu =\frac{3-\sqrt{5}}{2}\]
C) \[\mu =3+\sqrt{5}\]
D) \[\mu =\frac{1+\sqrt{5}}{2}\]
Correct Answer: A
Solution :
[a] Let refractive index of glass be\[\mu \]. Let after first refraction, image distance be v then \[\frac{\mu }{v}-\frac{1}{\infty }=\frac{\mu -1}{R}\Rightarrow v=\frac{\mu R}{\mu -1}\] Now second refraction will take place. So distance of first image from O is \[{{u}_{1}}=\frac{\mu R}{\mu -1}-R=\frac{R}{\mu -1}\] and image is formed at R \[\therefore \frac{1}{R}-\frac{\mu \left( \mu -1 \right)}{R}=\frac{2\left( 1-\mu \right)}{R}\] \[\Rightarrow {{\mu }^{2}}-3\mu +1=0\text{ So, }\mu =\frac{3+\sqrt{5}}{2}\]
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