Question

When you hold an insect at the near point of your eye it subtends an angle of 5.00 10-3 rad. Determine the maximum angular size of the insect when viewed through a magnifying glass (simple magnifier) that has a focal length of 8.70 cm.

Answer 1

Angle subtended by the insect at the near point of the eye = 5 * 10^-3 rad

This is taken as the angular size of the insect

Focal length of the magnifier is f = 8.70 cm

Distance to near point is generally taken as N = 25 cm. ( If not specified )

First the insect is seen with the help of unaided eye

Then the insect is seen with the help of magnifier so that image of the insect is formed at the near point.

Maximum angular size of the image of the insect at the near point be  '

Maximum angular size is possible when image of the object is at the near point

In such cases , magnification M = ( N / f ) + 1

= ( 25 / 8.7 ) + 1

= 2.873 + 1

= 3.873

Again , Magnification is given by

M = ' /

= ( angular size of the image when an optical instrument is used / angular size of the object when seen with unaided eye )

3.873 = ' / 5 * 10^-3

  ' = 3.873 × 5 × 10^-3

  ' = 19.365 * 10^-3 rad

So maximum angular size is 19.365 * 10^-3 rad