Lenses and Optical Instruments

$\boxed{\frac{1}{f} = \frac{1}{u} + \frac{1}{v}}$

Where:

• $f$ = focal length (m)
• $u$ = object distance (m)
• $v$ = image distance (m)

Sign Convention (Real-is-Positive)

• Real objects: $u$ is positive (light enters from left)
• Real images: $v$ is positive (form on opposite side to object)
• Virtual images: $v$ is negative (form on same side as object)
• Converging lens: $f$ is positive
• Diverging lens: $f$ is negative

$\boxed{m = \frac{v}{u} = \frac{\text{image height}}{\text{object height}}}$

• $|m| > 1$: magnified
• $|m| < 1$: diminished
• $m > 0$: upright (virtual)
• $m < 0$: inverted (real)

$P = \frac{1}{f}$

Units: dioptres (D). Converging: positive power. Diverging: negative power.

For lenses in contact: $P_{\text{total}} = P_1 + P_2$

The image from the first lens becomes the object for the second lens.

• Thin lens equation: $1/f = 1/u + 1/v$
• Sign convention: real positive, virtual negative
• $m = v/u$; power $P = 1/f$ (dioptres)
• Converging: $f > 0$; Diverging: $f < 0$