A) 15 cm
B) 20 cm
C) 30 cm
D) 10 cm
Correct Answer: C
Solution :
According to lens formula \[\frac{1}{f}=(\mu -1)\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\] The lens is plano-convex i.e., \[{{R}_{1}}=R\] and \[{{R}_{2}}=\infty \] Hence \[\frac{1}{f}=\frac{\mu -1}{R}\Rightarrow f=\frac{R}{\mu -1}\] Speed of light in medium of lens \[v=2\times {{10}^{8}}\] \[m/s\] Þ \[\mu =\frac{c}{v}=\frac{3\times {{10}^{8}}}{2\times {{10}^{8}}}=\frac{3}{2}=1.5\] If r is the radius and y is the thickness of lens (at the centre), the radius of curvature R of its curved surface in accordance with the figure is given by \[{{R}^{2}}={{r}^{2}}+{{(R-y)}^{2}}\Rightarrow {{r}^{2}}+{{y}^{2}}-2Ry=0\] Neglecting \[{{y}^{2}};\] we get \[R=\frac{{{r}^{2}}}{2y}=\frac{{{(6/2)}^{2}}}{2\times 0.3}=15\] cm Hence \[f=\frac{15}{1.5-1}=30\]You need to login to perform this action.
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