Simple Magnifiers: Angular Magnification and Viewing Arrangements

All flashcards

What is a simple magnifier?

A converging lens used with an object inside its focal length to produce an enlarged, upright, virtual image.

What does it mean for an image to be virtual?

The light rays do not meet at the image location; they only appear to come from there.

How is angular magnification defined?

It is the ratio of the image's angular size to the unaided object's angular size: $M = \theta_{\text{image}}/\theta_{\text{object}}$.

What is the general angular-magnification equation for a virtual-image viewing arrangement?

$M = (25\,\text{cm}/L)\left(1 + (L - \ell)/f\right)$, with $L$, $\ell$, and $f$ expressed in centimeters.

How does a magnifier's focal length affect its angular magnification?

For the stated viewing arrangements, a shorter focal length produces greater angular magnification.

Quiz questions

1. For a virtual-image viewing arrangement, which expression gives angular magnification when $L$, $\ell$, and $f$ are in centimeters?Answer: $M = (25\,\text{cm}/L)\left(1 + (L - \ell)/f\right)$
2. A magnifier with focal length $5.0\,\text{cm}$ is held close to the eye, with the virtual image at the $25\,\text{cm}$ near point. What is its angular magnification?Answer: $6.0$
3. For a simple magnifier whose virtual image is at infinity, what is the angular magnification?Answer: $M = 25\,\text{cm}/f$
4. In the described geometry, the eye is a distance $\ell$ from the lens and the virtual image is a distance $L$ from the eye. Under the usual thin-lens sign convention, what is the relation between image distance $d_i$ and these distances?Answer: $-d_i = L - \ell$
5. For near-point viewing with the magnifier close to the eye, what happens to angular magnification when the lens's focal length is shortened?Answer: It increases.