The lens equation uses the formula 1 1 1 f u v   and 150 mm u , 300 mm v . Without using mathematical tables or a calculator, determine the value of f.

The lens equation is: $1/f = 1/u + 1/v$
Given: u = 150 mm
Given: v = 300 mm

$1/f = 1/150 + 1/300$

The least common multiple of 150 and 300 is 300.
Convert $1/150$ to an equivalent fraction with a denominator of 300:
$1/150 = (1 \cdot 2) / (150 \cdot 2) = 2/300$

$1/f = 2/300 + 1/300$
$1/f = (2 + 1) / 300$
$1/f = 3/300$

Divide both the numerator and the denominator by their greatest common divisor, which is 3:
$1/f = (3 \div 3) / (300 \div 3)$
$1/f = 1/100$

Since $1/f = 1/100$, then f = 100 mm.