Question

A Two point sources (pixels) of monochromatic radiation can be resolved as close as 1.1 cm apart when viewing them at a distance of 1800 m through a lens 6 cm in diameter. What is the wavelength of the radiation? A) 3.005 times 10^-7 m B) 3.3 times 10^-7 m C) 6.6 times 10^-7 m D) 19.8 times 10^-7 m E) 5.94 times 10^-7 m A given individual is unable to see objects clearly when he is beyond 50 cm. What power lens should be used to correct this problem? A) -1.84 D B) -0.225 D C) -2 Diopters D) -7.843137 D E) -10.485437 D

Answer 1

3). Sources resolved by a distance, y= 1.1cm= 1.1*10^-2 m

Distance between screen and lens, D= 1800m

Diameter of lens, d= 6cm=6*10^-2m

Then using Young's double slit experiment, width of central fringe will be

$y= \frac{\lambda D}{d}$

$1.1 \times 10^{-2}= \frac{\lambda \times 1800}{6 \times 10^{-2}}$

$\lambda = 3.66 \times 10^{-7}m$(ANS)