Magnifying power

In geometric optics, the magnifying power (MP) is defined as the ratio of the angle subtended at the eye by the magnified view versus the unaided view. Note that the MP is different from the transverse magnification.

$$\text{MP}=\frac{{\alpha }_{\text{mag}}}{{\alpha }_{\text{unaided}}}$$

Note that the reason we don’t take the $\arctan$ is the small-angle approximation. The angles subtended are given by:

$${\alpha }_{\text{unaided}}=\frac{y_o}{D}$$ $${\alpha }_{\text{mag}}=\frac{y_i}{-s_i}=\frac{y_o}{s_o}$$

Where the numerator is the height of the object (not wrt the optical axis, just an absolute term), and the denominator is the distance away from the eye.

Abhay (the TA) suggests decomposing thee separately.

• First we find ${\alpha }_{\text{unaided}}$, then ${\alpha }_{\text{mag}}$.
• Usually the unaided angle is much more straightforward to compute (except with objects at an infinite distance).
• If we don’t necessarily have an unaided object size (i.e., $y_o$), we can put in a dummy variable that cancels out. In the magnified angle, the viewed object size is the result of $y_o$ times some magnification factor.

abs distance? sign convention?

-s_i is because the magnifying glass example is virtual image, so we need to make it positive y_o form is literally for pov of eye lmao i think D: near point of the eye s_o: distance from object to lens