A) 2.32 m
B) 4.28 mm
C) 1.25 cm
D) 12.48 cm
Correct Answer: C
Solution :
Key Idea: Angular limit of resolution of eye is the ratio of wavelength of light to diameter of eye lens. Angular limit of resolution of eye \[=\frac{Wavelength\,of\,light}{Diameter\,of\,eye\,lens}\] \[i.e.,\theta =\frac{\lambda }{d}...(i)\] If y is the minimum resolution between two objects at distance D from eye, then \[\theta =\frac{y}{D}....(ii)\] From Eqs. (i) and (ii), we have \[\frac{y}{D}=\frac{\lambda }{d}\] \[ory=\frac{\lambda D}{d}....(iii)\] Given, \[\lambda \] \[=5000\overset{\text{o}}{\mathop{\text{A}}}\,=5\times {{10}^{-7}}m,\,\,D=50\,m,\] \[d=2\,mm=2\times {{10}^{-3}}m\] Substituting in Eq. (iii), we get \[y=\frac{5\times {{10}^{-7}}\times 50}{2\times {{10}^{-3}}}\] \[=12.5\times {{10}^{-3}}\,m\] \[=1.25\,cm\]
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