Calculating the Angular Size of an Image with a Magnifying Glass

[kbray278]

Homework Statement

The near point of a naked eye is 33 cm. When an object is placed at the near point and viewed by the naked eye, it has an angular size of 0.060 rad. A magnifying glass has a focal length of 16 cm, and is held next to the eye. The enlarged image that is seen is located 51 cm from the magnifying glass. Determine the angular size of the image.

Homework Equations

Angular size=Theta(i)/Theta(o)

The Attempt at a Solution

Wasn't sure what to do

 

[rl.bhat]

angular size of the object αo = h/33. The angular size is given. Find the linear size h of the object.
Focal length of the glass and the image distance from the magnifying glass is given. From that find the object distance so
The angular size of the image = h/so.

 

[ideasrule]

angular size of the object αo = h/33. The angular size is given. Find the linear size h of the object.
Focal length of the glass and the image distance from the magnifying glass is given. From that find the object distance so
The angular size of the image = h/so.

To clarify, height of image/distance of image (which you want to find) = height of object/distance of object. This can easily be seen with a ray diagram.

 

[rl.bhat]

To clarify, height of image/distance of image (which you want to find) = height of object/distance of object. This can easily be seen with a ray diagram.

In this problem size of the image is irrelevant. You have to bring the object closer to the eye to make its angular size larger to see its details clearly. Because of the limitation of the accommodation of the eye, we cannot see the object clearly. To see the object in the same position, we have to use magnifying glass which forms its image at near point.