Question

Using Rayleigh's criterion, calculate the diameter of an earth-based telescope that gives this resolution with 700 nm light.

Answer 1

Complete Question

Due to blurring caused by atmospheric distortion, the best resolution that can be obtained by a normal, earth-based, visible-light telescope is about 0.3 arcsecond (there are 60 arcminutes in a degree and 60 arcseconds in an arcminute).Using Rayleigh's criterion, calculate the diameter of an earth-based telescope that gives this resolution with 700 nm light

Answer:

The diameter is
`D = 0.59 \ m`

Step-by-step explanation:

From the question we are told that

The best resolution is
`\theta = 0.3 \ arcsecond`

The wavelength is
`\lambda = 700 \ nm = 700 *10^(-9 ) \ m`

Generally the

1 arcminute = > 60 arcseconds

=> x arcminute => 0.3 arcsecond

So

`x = (0.3)/(60 )`

=>
`x = 0.005 \ arcminutes`

Now

60 arcminutes => 1 degree

0.005 arcminutes = > z degrees

=>
`z = (0.005)/(60 )`

=>
`z = 8.333 *10^(-5) \ degree`

Converting to radian

`\theta = z = 8.333 *10^(-5) * 0.01745 = 1.454 *10^(-6) \ radian`

Generally the resolution is mathematically represented as

`\theta = (1.22 * \lambda )/( D)`

=>
`D = (1.22 * \lambda )/(\theta )`

=>
`D = (1.22 * 700 *10^(-9) )/( 1.454 *10^(-6) )`

=>
`D = 0.59 \ m`