# Optics: radius of a central disk of light

1. Aug 9, 2010

### vorcil

1. The problem statement, all variables and given/known data

A telescope objective is 12cm in diameter and has a focal length of 150cm.

Light of mean wavelength 550nm from a distant star enters the scope as a nearly collimated beam.

compute the radius of the central disk of light forming the image of the star on the focal plane of the lens

2. Relevant equations

$$\theta_{min\frac{1}{2}} = \frac{1.22*\lambda}{D}$$

Radius of disk =$$L * \theta_{min\frac{1}{2}}$$

3. The attempt at a solution

after showing the proof for those equations all I did was solve for the radius of the disk by plugging in the numbers,

$$\frac{1.22 * (550*(10^{-9}))}{\frac{12}{100}m}*\frac{150}{100}m$$

putting into a calculator I got 8.3875*10^-6, approximately 8.39*10^-6

what am I missing?