Question

Two point sources (pixels) of monochromatic radiation can be resolved as close as 0.3 cm apart when viewing them at a distance of 1500 m through a lens 7 cm in diameter. What is the wavelength of the radiation? A) 2.1 X 10^-7 m B) 6 .3 x 10^-7 m C) 1.148 X 10^-7 m D) 0.643 X 10^-7 m E) 1.35 x 10^-7 m

Answer 1

Wavelength,
`\lambda=1.148* 10^(-7)\ m`

Step-by-step explanation:

It is given that,

Two point sources (pixels) of monochromatic radiation can be resolved as close as 0.3 cm apart, x = 0.3 cm = 0.003 m

Diameter of lens, d = 7 cm = 0.07 m

Distance from the view line, D = 1500 m

We need to find the wavelength of the radiation. The formula for resolving power of Rayleigh criterion is given by :

`d=(1.22\lambda D)/(x)`

`\lambda=(xd)/(1.22D)`

`\lambda=(0.003* 0.07)/(1.22* 1500)`

`\lambda=1.148* 10^(-7)\ m`

So, the wavelength of the radiation is
`1.148* 10^(-7)\ m`. Hence, this is the required solution.