Optics: radius of a central disk of light

[vorcil]

Homework Statement

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

Homework Equations

[tex] \theta_{min\frac{1}{2}} = \frac{1.22*\lambda}{D} [/tex]

Radius of disk =[tex] L * \theta_{min\frac{1}{2}} [/tex]

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,

[tex] \frac{1.22 * (550*(10^{-9}))}{\frac{12}{100}m}*\frac{150}{100}m [/tex]

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

however the answers show 8.39*10^-4,

what am I missing?

 

[mark726]

It seems like you may have missed a conversion from meters to centimeters in your calculation. The diameter of the telescope objective is given in centimeters, so you should convert the focal length from meters to centimeters before plugging it into the equation. This would give a value of 1.5 cm instead of 150 cm. Plugging that into the equation, you should get a radius of 8.39*10^-4 cm, which matches the given answer.